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Concept in convex optimization mathematics
Subgradient methods are convex optimization methods which use subderivatives. Originally developed by Naum Z. Shor and others in the 1960s and 1970s,
Subgradient_method
Subfield of mathematical optimization
functions. Cutting-plane methods Ellipsoid method Subgradient method Dual subgradients and the drift-plus-penalty method Subgradient methods can be implemented
Convex_optimization
Algorithm for finding zeros of functions
extrapolation Root-finding algorithm Secant method Steffensen's method Subgradient method Fowler, David; Robson, Eleanor (1998). "Square root approximations
Newton's_method
Algorithm for linear programming
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is an algorithm for linear programming. The name of the algorithm is derived
Simplex_algorithm
Statistical optimization technique
he first proposed a new method of locating the maximum point of an arbitrary multipeak curve in a noisy environment. This method provided an important theoretical
Bayesian_optimization
Optimization technique for solving (mixed) integer linear programs
and bundle methods. They are popularly used for non-differentiable convex minimization, where a convex objective function and its subgradient can be evaluated
Cutting-plane_method
Optimization algorithm
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate
Gradient_descent
Method of solving linear programming problems
operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm. The Big M method extends the simplex algorithm
Big_M_method
Soviet and Ukrainian mathematician
known for his method of generalized gradient descent with space dilation in the direction of the difference of two successive subgradients (the so-called
Naum_Z._Shor
Study of mathematical algorithms for optimization problems
Subgradient methods: An iterative method for large locally Lipschitz functions using generalized gradients. Following Boris T. Polyak, subgradient–projection
Mathematical_optimization
Algorithms for solving convex optimization problems
Interior-point methods (also referred to as barrier methods or IPMs) are algorithms for solving linear and non-linear convex optimization problems. IPMs
Interior-point_method
Method to solve optimization problems
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical
Linear_programming
Sequence of locally optimal choices
optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling
Greedy_algorithm
Numerical optimization algorithm
The Nelder–Mead method (also downhill simplex method, amoeba method, or polytope method) is a numerical method used to find a local minimum or maximum
Nelder–Mead_method
Class of algorithms for solving constrained optimization problems
Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they
Augmented_Lagrangian_method
Iterative method for minimizing convex functions
(that is: compute the value of f(x) and a subgradient f'(x)). Under these assumptions, the ellipsoid method is "R-polynomial". This means that there exists
Ellipsoid_method
Algorithm used to solve non-linear least squares problems
algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization
Levenberg–Marquardt_algorithm
Generalization of derivatives to real-valued functions
In mathematics, the subderivative (or subgradient) generalizes the derivative to convex functions which are not necessarily differentiable. The set of
Subderivative
Numerical approximation algorithm
method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of an iterative method or a method of
Iterative_method
Optimization algorithm
In numerical analysis, a quasi-Newton method is an iterative numerical method used either to find zeroes or to find local maxima and minima of functions
Quasi-Newton_method
Statistical method
include coordinate descent, subgradient methods, least-angle regression (LARS), and proximal gradient methods. Subgradient methods are the natural generalization
Lasso_(statistics)
Mathematical discipline
(including Luus–Jaakola) Simulated annealing Stochastic optimization Subgradient method various model-based algorithms like BOBYQA and ORBIT There exist benchmarks
Derivative-free_optimization
Collective behavior of decentralized, self-organized systems
systems. Their simulations showed the social potential fields method is robust in that the method can tolerate errors in sensors and actuators. The Social
Swarm_intelligence
Mathematical function with convex lower level sets
"efficient" methods use "divergent-series" step size rules, which were first developed for classical subgradient methods. Classical subgradient methods using
Quasiconvex_function
Optimization algorithm
604861. Kiwiel, Krzysztof C. (2001). "Convergence and efficiency of subgradient methods for quasiconvex minimization". Mathematical Programming, Series A
Stochastic_gradient_descent
Optimization algorithm
LM-BFGS) is an optimization algorithm in the collection of quasi-Newton methods that approximates the Broyden–Fletcher–Goldfarb–Shanno algorithm (BFGS)
Limited-memory_BFGS
Type of algorithm for constrained optimization
optimization, penalty methods are a certain class of algorithms for solving constrained optimization problems. A penalty method replaces a constrained
Penalty_method
Optimization algorithm
known as the conditional gradient method, reduced gradient algorithm and the convex combination algorithm, the method was originally proposed by Marguerite
Frank–Wolfe_algorithm
Optimization algorithm
finding good paths through graphs. Artificial ants represent multi-agent methods inspired by the behavior of real ants. The pheromone-based communication
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Problem optimization method
programming (DP) is both a mathematical optimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s and has
Dynamic_programming
Optimization algorithm
The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method. The step size can be determined either exactly
Line_search
Optimization by removing non-optimal solutions to subproblems
Branch-and-bound (BB, B&B, or BnB) is a method for solving optimization problems by breaking them down into smaller subproblems and using a bounding function
Branch_and_bound
Mathematical optimization problem restricted to integers
the branch and bound method. For example, the branch and cut method that combines both branch and bound and cutting plane methods. Branch and bound algorithms
Integer_programming
Continuous function whose value increases to infinity
functions was motivated by their connection with primal-dual interior point methods. Consider the following constrained optimization problem: minimize f(x)
Barrier_function
Linear programming algorithm
the revised simplex method is a variant of George Dantzig's simplex method for linear programming. The revised simplex method is mathematically equivalent
Revised_simplex_method
Subfield of mathematical optimization
Chakrabarti, Bikas K, eds. (2005). Quantum Annealing and Related Optimization Methods. Lecture Notes in Physics. Vol. 679. Springer. Bibcode:2005qnro.book..
Combinatorial_optimization
Optimizing objective functions that have constrained variables
constrained case, often via the use of a penalty method. However, search steps taken by the unconstrained method may be unacceptable for the constrained problem
Constrained_optimization
Subfield of convex optimization
case of cone programming and can be efficiently solved by interior point methods. All linear programs and (convex) quadratic programs can be expressed as
Semidefinite_programming
Local search algorithm
Tabu search (TS) is a metaheuristic search method employing local search methods used for mathematical optimization. It was created by Fred W. Glover
Tabu_search
Primal-Dual algorithm optimization for convex problems
{\displaystyle \partial F^{*}} and ∂ G {\displaystyle \partial G} are the subgradient of the convex functions F ∗ {\displaystyle F^{*}} and G {\displaystyle
Chambolle–Pock_algorithm
Optimization method
algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like the related Davidon–Fletcher–Powell method, BFGS determines the
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Types generalized of derivatives
f : Y → R . {\displaystyle f:Y\to \mathbb {R} .} Subgradient method — Class of optimization methods for nonsmooth functions. Subderivative Clarke, F.
Clarke_generalized_derivative
Optimization algorithm
programming (SQP) is an iterative method for constrained nonlinear optimization, also known as Lagrange-Newton method. SQP methods are used on mathematical problems
Sequential quadratic programming
Sequential_quadratic_programming
Optimization algorithm
better neighbour is generated, in which this neighbour is then chosen. This method performs well when states have many possible successors (e.g. thousands)
Hill_climbing
Optimization technique
problems. Their use is always of interest when exact or other (approximate) methods are not available or are not expedient, either because the calculation
Metaheuristic
Mathematical algorithm
Study of mathematical algorithms for optimization problems Newton's method – Method for finding stationary points of a function Stochastic gradient descent –
Coordinate_descent
Technique for finding an extremum of a function
boundary of the interval, it will converge to that boundary point. The method operates by successively narrowing the range of values on the specified
Golden-section_search
Solution process for some optimization problems
to the higher computational load and little theoretical benefit. Another method involves the use of branch and bound techniques, where the program is divided
Nonlinear_programming
Algorithm in computer science
optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling
Artificial bee colony algorithm
Artificial_bee_colony_algorithm
Type of infinite structure
guarantee the convergence of some non-smooth optimization methods, such as the stochastic subgradient method (under some mild assumptions). Semialgebraic set Real
O-minimal_theory
Linear programming algorithm
algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice. Denoting
Karmarkar's_algorithm
Iterative optimisation algorithm
Powell's dog leg method, also called Powell's hybrid method, is an iterative optimisation algorithm for the solution of non-linear least squares problems
Powell's_dog_leg_method
Mathematical algorithm for eliminating variables from a system of linear inequalities
Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities.
Fourier–Motzkin_elimination
Class of algorithms that find approximate solutions to optimization problems
algorithmic techniques for these formulations are applied. Rounding-based methods. This involves solving the considered formulation for a good fractional
Approximation_algorithm
Mathematical optimization algorithms
The truncated Newton method, originated in a paper by Ron Dembo and Trond Steihaug, also known as Hessian-free optimization, are a family of optimization
Truncated_Newton_method
Inequalities for inexact line search
especially in quasi-Newton methods, first published by Philip Wolfe in 1969 (also named after Larry Armijo). In these methods the idea is to find min x
Wolfe_conditions
Solving an optimization problem with a quadratic objective function
definite. It is possible to write a variation on the conjugate gradient method which avoids the explicit calculation of Z. The Lagrangian dual of a quadratic
Quadratic_programming
Algorithm for finding a local minimum of a function
Powell's method, strictly Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a function
Powell's_method
In optimization, a gradient method is an algorithm to solve problems of the form min x ∈ R n f ( x ) {\displaystyle \min _{x\in \mathbb {R} ^{n}}\;f(x)}
Gradient_method
Term in mathematical optimization
reasonable approximation. Trust-region methods are in some sense dual to line-search methods: trust-region methods first choose a step size (the size of
Trust_region
Mathematical combinatorial optimization method
many variables. The method is a hybrid of branch and bound and column generation methods. Branch and price is a branch and bound method in which at each
Branch_and_price
Subset of a function's domain on which its value is equal
3570770. Kiwiel, Krzysztof C. (2001). "Convergence and efficiency of subgradient methods for quasiconvex minimization". Mathematical Programming, Series A
Level_set
Algorithm to compute the maximum flow in a flow network
the Edmonds–Karp algorithm is an implementation of the Ford–Fulkerson method for computing the maximum flow in a flow network in O ( | V | | E | 2 )
Edmonds–Karp_algorithm
Algorithm for computing the maximal flow of a network
optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling
Dinic's_algorithm
Population-based search algorithm
D. T., Castellani M., A modified Bees Algorithm and a statistics-based method for tuning its parameters. Proceedings of the Institution of Mechanical
Bees_algorithm
Branch of mathematical optimization
optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling
Discrete_optimization
Combinatorial optimization method
Branch and cut is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some
Branch_and_cut
Form of Newton's method used in statistics
Scoring algorithm, also known as Fisher's scoring, is a form of Newton's method used in statistics to solve maximum likelihood equations numerically, named
Scoring_algorithm
Optimization algorithm
abandoned nests (instead of using the random replacements from the original method). Modifications to the algorithm have also been made by additional interbreeding
Cuckoo_search
Algorithm for solving the quadratic programming problem from training SVMs
called Bregman methods or row-action methods. These methods solve convex programming problems with linear constraints. They are iterative methods where each
Sequential minimal optimization
Sequential_minimal_optimization
Solving multiple machine learning tasks at the same time
auxiliary tasks and combining losses of all tasks in a useful way. Some methods can learn these from data together with the training process, and combine
Multi-task_learning
of objective function in sum of possible non-differentiable pieces Subgradient method — extension of steepest descent for problems with a non-differentiable
List of numerical analysis topics
List_of_numerical_analysis_topics
Sequential linear-quadratic programming (SLQP) is an iterative method for nonlinear optimization problems where objective function and constraints are
Sequential linear-quadratic programming
Sequential_linear-quadratic_programming
Computer compiler optimization technique
the "global" approach, which operates over the whole compilation unit (a method or procedure for instance). Graph-coloring allocation is the predominant
Register_allocation
Quantum physics-based metaheuristic for optimization problems
Sebenik, C.; Stenson, C.; Doll, J. D. (1994). "Quantum annealing: A new method for minimizing multidimensional functions". Chemical Physics Letters. 219
Quantum_annealing
Econometric Modelling with Time Series, Chapter 3 'Numerical Estimation Methods'. Cambridge University Press, 2015. Amemiya, Takeshi (1985). Advanced Econometrics
Berndt–Hall–Hall–Hausman algorithm
Berndt–Hall–Hall–Hausman_algorithm
Concept in mathematics
numerical optimization, the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization. For a quadratic function
Nonlinear conjugate gradient method
Nonlinear_conjugate_gradient_method
have a "subgradient oracle": a routine that can compute a subgradient of f at any given point (if f is differentiable, then the only subgradient is the
Center-of-gravity_method
Optimization method
the curvature condition. It was the first quasi-Newton method to generalize the secant method to a multidimensional problem. This update maintains the
Davidon–Fletcher–Powell formula
Davidon–Fletcher–Powell_formula
Israeli-American computer scientist
the co-inventor of five US patents. Hazan co-introduced adaptive subgradient methods to dynamically incorporate knowledge of the geometry of the data
Elad_Hazan
Optimization algorithm
optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling
Spiral_optimization_algorithm
Methods in numerical computation
Rosenbrock methods refers to either of two distinct ideas in numerical computation, both named for Howard H. Rosenbrock. Rosenbrock methods for stiff differential
Rosenbrock_methods
Method in mathematical optimization
Lindberg, P. O. (August 2007). "Lagrangian relaxation via ballstep subgradient methods". Mathematics of Operations Research. 32 (3): 669–686. doi:10.1287/moor
Lagrangian_relaxation
Chinese scientist and revolutionary (born 1961)
optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling
Liu_Gang
Metaheuristic proposed by Xin-She Yang
optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling
Firefly_algorithm
Crucial concept of quantum information
optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling
Incompatibility of quantum measurements
Incompatibility_of_quantum_measurements
form or the other. De Jong's crowding method, Goldberg's sharing function approach, Petrowski's clearing method, restricted mating, maintaining multiple
Evolutionary multimodal optimization
Evolutionary_multimodal_optimization
Special case of discrete optimization
Special order sets are basically a device or tool used in branch and bound methods for branching on sets of variables, rather than individual variables, as
Special_ordered_set
Concept in mathematics
Multiplicative weight update method Hedge algorithm Bregman divergence Arkadi Nemirovsky and David Yudin. Problem Complexity and Method Efficiency in Optimization
Mirror_descent
Guided local search is a metaheuristic search method. A meta-heuristic method is a method that sits on top of a local search algorithm to change its behavior
Guided_local_search
The Symmetric Rank 1 (SR1) method is a quasi-Newton method to update the second derivative (Hessian) based on the derivatives (gradients) calculated at
Symmetric_rank-one
Algorithm for solving linear programs
so the optimal solution can be found without them. In many cases, this method allows to solve large linear programs that would otherwise be intractable
Column_generation
numerical optimization is the use of one optimization method to tune another optimization method. Meta-optimization is reported to have been used as early
Meta-optimization
optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling
Bat_algorithm
traditionally used to tackle these problems: exact methods and metaheuristics.[disputed – discuss] Exact methods allow to find exact solutions but are often
Parallel_metaheuristic
optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling
Fireworks_algorithm
mirror variables equal the original variables. The disadvantage of this method is that the number of variables and constraints is much larger than the
Distributed constraint optimization
Distributed_constraint_optimization
Principle in mathematical optimization
Lindberg, P. O. (August 2007). "Lagrangian relaxation via ballstep subgradient methods". Mathematics of Operations Research. 32 (3): 669–686. doi:10.1287/moor
Duality_(optimization)
Approximation for nonlinear optimization
related to, but distinct from, quasi-Newton methods. Starting at some estimate of the optimal solution, the method is based on solving a sequence of first-order
Successive_linear_programming
optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling
Brain storm optimization algorithm
Brain_storm_optimization_algorithm
SUBGRADIENT METHOD
SUBGRADIENT METHOD
Boy/Male
Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Boy/Male
English American
From the west meadow. John and Charles Wesley were the founders of Methodism.
Surname or Lastname
Americanized form of German Albrecht.English
Americanized form of German Albrecht.English : from a medieval variant of the personal name Albert.Jacob Albright (1759–1808), a prominent Methodist preacher, was born in Pottstown, PA, the son of a German immigrant called Johann Albrecht.
Girl/Female
Tamil
Method, Wealth, Protection, Conduct, Auspiciousness, Memory, Well being
Boy/Male
Indian
Method, Way, Mode, Manner, One who crosses the river of life, Morning star
Surname or Lastname
English
English : topographic name from Middle English lang, long ‘long’ + strete ‘road’.Translation of Dutch Langestraet, cognate with 1.The confederate general James Longstreet (1821–1904), was born in SC, came from an old Dutch family in New Netherland with the name Langestraet; he was the nephew of Augustus B. Longstreet, a Methodist clergyman born in Augusta, GA, in 1790.
Boy/Male
Indian
Method, Way, Mode, Manner, One who crosses the river of life, Morning star
Boy/Male
Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Male
Greek
(Μεθόδιος) Greek name derived from methodos, METHODIOS means "method."
Surname or Lastname
English (Devon)
English (Devon) : habitational name from a place so called in Hatherleigh, Devon.The Methodist Robert Strawbridge was born in Drummersnave (now Drumsna), near Carrick-on-Shannon, Co. Leitrim, Ireland. Some time between 1759 and 1766 he emigrated to MD and settled on Sam’s Creek, Frederick Co.
Boy/Male
Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Boy/Male
Tamil
Method, Way, Mode, Manner, One who crosses the river of life, Morning star
Boy/Male
Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Boy/Male
Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Boy/Male
Tamil
Vedhanth | வேதாநà¯à®¤
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Vedhanth | வேதாநà¯à®¤
Surname or Lastname
English (of Norman origin) and French
English (of Norman origin) and French : status name for a professional champion, especially an agent employed to represent one of the parties in a trial by combat, a method of settling disputes current in the Middle Ages. The word comes from Old French champion, campion (Late Latin campio, genitive campionis, a derivative of campus ‘plain’, ‘field of battle’). Compare Campion, Kemp.
Girl/Female
Tamil
Method, Wealth, Protection, Conduct, Auspiciousness, Memory, Well being
Boy/Male
Muslim
Method, Way, Mode, Manner, One who crosses the river of life, Morning star
Boy/Male
Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Boy/Male
Muslim
Method, Way, Mode, Manner, One who crosses the river of life, Morning star
SUBGRADIENT METHOD
SUBGRADIENT METHOD
Boy/Male
American, British, Dutch, English, French, German, Greek
Manly; Brave
Girl/Female
American, British, English
Combination of Kay and Lynn; Keeper of the Keys; Pure
Boy/Male
American, British, English
Rich and Powerful Ruler
Girl/Female
Assamese, Hindu, Indian, Marathi
Star
Boy/Male
Muslim
Name of a sahabi who participated in the battle of Badr
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sikh, Telugu
The Moon
Boy/Male
Hindu
Name of Lord Shiva
Surname or Lastname
Austrian and Swiss German
Austrian and Swiss German : a variant spelling of Hänni, see Hanni.English : variant spelling of Hanney.
Girl/Female
Tamil
Divine, Grand
Girl/Female
Muslim/Islamic
She lived between -
SUBGRADIENT METHOD
SUBGRADIENT METHOD
SUBGRADIENT METHOD
SUBGRADIENT METHOD
SUBGRADIENT METHOD
n.
An orderly procedure or process; regular manner of doing anything; hence, manner; way; mode; as, a method of teaching languages; a method of improving the mind.
a.
Alt. of Methodical
a.
Of or pertaining to the ancient school of physicians called methodists.
a.
Alt. of Methodistical
imp. & p. p.
of Methodize
n.
One of a sect of Christians, the outgrowth of a small association called the "Holy Club," formed at Oxford University, A.D. 1729, of which the most conspicuous members were John Wesley and his brother Charles; -- originally so called from the methodical strictness of members of the club in all religious duties.
n.
The system of doctrines, polity, and worship, of the sect called Methodists.
n.
The act or process of methodizing, or the state of being methodized.
n.
Classification; a mode or system of classifying natural objects according to certain common characteristics; as, the method of Theophrastus; the method of Ray; the Linnaean method.
n.
One who methodizes.
n.
The science of method or arrangement; a treatise on method.
p. pr. & vb. n.
of Methodize
n.
One who observes method.
n.
The art and principles of method.
a.
Of or pertaining to methodists, or to the Methodists.
a.
Of or pertaining to methodology.
a.
Proceeding with regard to method; systematic.
v. t.
To reduce to method; to dispose in due order; to arrange in a convenient manner; as, to methodize one's work or thoughts.
a.
Of or pertaining to the sect of Methodists; as, Methodist hymns; a Methodist elder.
a.
Arranged with regard to method; disposed in a suitable manner, or in a manner to illustrate a subject, or to facilitate practical observation; as, the methodical arrangement of arguments; a methodical treatise.