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Optimization technique for solving (mixed) integer linear programs
In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective
Cutting-plane_method
Concept in integral mathematics
cut method combines the cutting plane and branch and bound methods. In any subproblem, it runs the cutting plane method until no more cutting planes can
Linear_programming_relaxation
Algorithm for linear programming
Pivoting rule of Bland, which avoids cycling Criss-cross algorithm Cutting-plane method Devex algorithm Fourier–Motzkin elimination Gradient descent Karmarkar's
Simplex_algorithm
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
Branch of mathematics
approximation, the polyhedra contain the set. The cutting-plane method is an umbrella term for optimization methods which iteratively refine a feasible set or
Global_optimization
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
Optimization by removing non-optimal solutions to subproblems
Backtracking Branch-and-cut, a hybrid between branch-and-bound and the cutting plane methods that is used extensively for solving integer linear programs. Evolutionary
Branch_and_bound
Sequential model-based optimization of expensive black-box functions
or unreliable. The objective need not have a closed-form expression. The method constructs a probabilistic model of the unknown function, often a Gaussian
Bayesian_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
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
Method to solve optimization problems
Advanced algorithms for solving integer linear programs include: cutting-plane method Branch and bound Branch and cut Branch and price if the problem has
Linear_programming
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
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 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
Algorithm for finding zeros of functions
In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding
Newton's_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
Iterative method for minimizing convex functions
_{(k)}^{-1}\left(x-x^{(k)}\right)\leqslant 1\right\}.} We query the cutting-plane oracle to obtain a vector g ( k + 1 ) ∈ R n {\displaystyle g^{(k+1)}\in
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
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
Study of mathematical algorithms for optimization problems
to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general
Mathematical_optimization
NP-hard problem in combinatorial optimization
developed the cutting plane method for its solution. They wrote what is considered the seminal paper on the subject in which, with these new methods, they solved
Travelling_salesman_problem
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
Combinatorial optimization method
Branch and cut involves running a branch and bound algorithm and using cutting planes to tighten the linear programming relaxations. Note that if cuts are
Branch_and_cut
Optimization algorithm
doi:10.1016/S0166-218X(01)00351-1. J. M. Belenguer, and E. Benavent, "A cutting plane algorithm for capacitated arc routing problem," Computers & Operations
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
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
Sequence of locally optimal choices
Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine
Greedy_algorithm
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
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
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
Subfield of mathematical optimization
Chinese postman problem Closure problem Constraint satisfaction problem Cutting stock problem Dominating set problem Integer programming Job shop scheduling
Combinatorial_optimization
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Algorithm for computing the maximal flow of a network
Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine
Dinic's_algorithm
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
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
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
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
Mathematical combinatorial optimization method
relatively easy to solve. If cutting planes are used to tighten LP relaxations within a branch and price algorithm, the method is known as branch price and
Branch_and_price
Black-box description of a convex set
separation oracle (also called a cutting-plane oracle) is a concept in the mathematical theory of convex optimization. It is a method to describe a convex set
Separation_oracle
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
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
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
Primal-Dual algorithm optimization for convex problems
Antonin Chambolle and Thomas Pock in 2011 and has since become a widely used method in various fields, including image processing, computer vision, and signal
Chambolle–Pock_algorithm
American mathematician (1916–1996)
George Dantzig and D. R. Fulkerson, Johnson pioneered the use of cutting-plane methods for integer linear programming in solving the travelling salesman
Selmer_M._Johnson
Suite of mathematical modeling and optimization tools
branch and bound method and the cutting-plane method. Infeasible problems can be analyzed via the IIS (irreducible infeasible subset) method. Xpress provides
FICO_Xpress
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
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
Tool for working with wood
A hand plane is a tool for shaping wood using muscle power to force the cutting iron (blade) over the wood surface. Some rotary power planers are motorized
Plane_(tool)
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
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
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
Metaheuristic proposed by Xin-She Yang
Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine
Firefly_algorithm
Algorithm for solving linear programs
The classical example of a problem where it is successfully used is the cutting stock problem. One particular technique in linear programming which uses
Column_generation
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
Extended Frege system Polynomial calculus Nullstellensatz system Cutting-plane method Semantic tableau Cook, Stephen; Reckhow, Robert A. (1979). "The Relative
Propositional_proof_system
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
Means by which a person dies by suicide
every suicide by wrist cutting, there are many more nonfatal attempts, so that the number of actual deaths using this method is very low. Wounds from
Suicide_methods
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
Algorithm in computer science
Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine
Artificial bee colony algorithm
Artificial_bee_colony_algorithm
Algorithm in mathematical optimization
Cherkassky, Boris V.; Goldberg, Andrew V. (1995). "On implementing push-relabel method for the maximum flow problem". Integer Programming and Combinatorial Optimization
Push–relabel maximum flow algorithm
Push–relabel_maximum_flow_algorithm
Unit hypercube of variable dimension whose corners have been perturbed
Bland, Robert G. (May 1977). "New finite pivoting rules for the simplex method". Mathematics of Operations Research. 2 (2): 103–107. doi:10.1287/moor.2
Klee–Minty_cube
the objective function and the constraint set can be biconvex. There are methods that can find the global optimum of these problems. A set B ⊂ X × Y {\displaystyle
Biconvex_optimization
Quasi-infinite number in mathematics
grossone-based method for lexicographic multi-objective linear programming. Later work by Cococcioni and collaborators proposed a cutting-plane method for lexicographic
Grossone
Chinese scientist and revolutionary (born 1961)
Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine
Liu_Gang
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
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
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
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
all the unknowns are restricted to integer values Branch and cut Cutting-plane method Karmarkar's algorithm: The first reasonably efficient algorithm that
List_of_algorithms
Branch of mathematical optimization
Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine
Discrete_optimization
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
and versatile method of gear cutting. It involves continuous, same-plane rotational cutting of gear. Other methods of gear tooth cutting include Hobbing
Gear_shaping
Crucial concept of quantum information
Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine
Incompatibility of quantum measurements
Incompatibility_of_quantum_measurements
Type of optimization heuristic
104–115 (2000) Stefan Boettcher, Allon G. Percus, "Extremal Optimization: Methods derived from Co-Evolution", Proceedings of the Genetic and Evolutionary
Extremal_optimization
Optimization algorithm
Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine
Spiral_optimization_algorithm
Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine
Bat_algorithm
rider optimization algorithm (ROA) is devised based on a novel computing method, namely fictional computing that undergoes series of process to solve the
Rider_optimization_algorithm
German mathematician (born 1948)
of solution methods of the Traveling Salesman Problem, in particular, he contributed significantly to understanding the cutting-plane method. His publications
Martin_Grötschel
Method for mathematical optimization
calculated parts of a tableau, if implemented like the revised simplex method). In a general step, if the tableau is primal or dual infeasible, it selects
Criss-cross_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
Industrial tool
searched for new methods of efficient cutting systems. In 1956, Carl Johnson of Durox International in Luxembourg developed a method for cutting plastic shapes
Water_jet_cutter
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
Cutting Plane Method and its Implications for Combinatorial and Convex Optimization" 2014 Aaron Sidford (MIT) Yin Tat Lee (MIT) "Path-Finding Methods
Machtey_Award
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
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