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Problem of finding the best feasible solution
and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into
Optimization_problem
Study of mathematical algorithms for optimization problems
generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from
Mathematical_optimization
Subfield of mathematical optimization
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the
Combinatorial_optimization
Mathematical concept
multiattribute optimization) is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously
Multi-objective_optimization
Subfield of mathematical optimization
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently
Convex_optimization
Optimizing objective functions that have constrained variables
In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function
Constrained_optimization
Principle in mathematical optimization
In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives
Duality_(optimization)
Mathematical method for optimizing material layout under given conditions
the performance of the system. Topology optimization is different from shape optimization and sizing optimization in the sense that the design can attain
Topology_optimization
Problem in combinatorial optimization
The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items
Knapsack_problem
Process of developing trajectory performance
the trajectory optimization problem (optimizing over functions) is converted into a constrained parameter optimization problem (optimizing over real numbers)
Trajectory_optimization
Iterative simulation method
In computational science, particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a population
Particle_swarm_optimization
Optimization algorithms using quantum computing
Quantum optimization algorithms are quantum algorithms that are used to solve optimization problems. Mathematical optimization deals with finding the best
Quantum optimization algorithms
Quantum_optimization_algorithms
Optimization algorithm
operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems that can be reduced to finding
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Necessary condition for optimality associated with dynamic programming
Bellman, is a technique in dynamic programming which breaks an optimization problem into a sequence of simpler subproblems, as Bellman's "principle of
Bellman_equation
Combinatorial optimization problem
unconstrained binary optimization (QUBO), also known as unconstrained binary quadratic programming (UBQP), is a combinatorial optimization problem with a wide
Quadratic unconstrained binary optimization
Quadratic_unconstrained_binary_optimization
Solution process for some optimization problems
programming (NLP), also known as nonlinear optimization, is the process of solving an optimization problem where some of the constraints are not linear
Nonlinear_programming
Mathematical problem in operations research
It is an optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard
Cutting_stock_problem
On short connecting nets with added points
tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization. While
Steiner_tree_problem
Sequence of operations for a task
are greedy algorithms that can solve this optimization problem. The heuristic method In optimization problems, heuristic algorithms find solutions close
Algorithm
Functions used to evaluate optimization algorithms
optimization cases are presented. In the second part, test functions with their respective Pareto frontiers for multi-objective optimization problems
Test functions for optimization
Test_functions_for_optimization
Topics referred to by the same term
been studied from various angles. Optimal facility location is an optimization problem: deciding where to place the facility in order to minimize transportation
Facility_location_problem
Complexity class
routing Scheduling Problems that are decidable but not NP-complete, often are optimization problems: Knapsack optimization problems Integer programming
NP-hardness
Method for problem solving in optimization
heuristic method for solving computationally hard optimization problems. Local search can be used on problems that can be formulated as finding a solution
Local_search_(optimization)
Subset of a graph's vertices, including at least one endpoint of every edge
the graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization problem. It is NP-hard, so it cannot be solved
Vertex_cover
Optimization problem
Stigler diet is an optimization problem named for George Stigler, a 1982 Nobel laureate in economics, who posed the following problem: For a moderately
Stigler_diet
Mathematical optimization theory
Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought
Robust_optimization
Design optimization is an engineering design methodology using a mathematical formulation of a design problem to support selection of the optimal design
Design_optimization
Method of mathematical optimization
the problem being optimized, which means DE does not require the optimization problem to be differentiable, as is required by classic optimization methods
Differential_evolution
Process of selecting a portfolio
minimizes costs like financial risk, resulting in a multi-objective optimization problem. Factors being considered may range from tangible (such as assets
Portfolio_optimization
Quadratic fractional programming problem
Bilevel optimization is a special kind of optimization where one problem is embedded (nested) within another. The outer optimization task is commonly referred
Bilevel_optimization
NP-hard problem in combinatorial optimization
NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem, the vehicle
Travelling_salesman_problem
Yes/no problem in computer science
decision problem to be studied; and in many cases the original function or optimization problem can be solved by solving its corresponding decision problem. For
Decision_problem
Sequential model-based optimization of expensive black-box functions
Bayesian optimization is a sequential model-based strategy for global optimization of black-box objective functions whose evaluations are costly. It is
Bayesian_optimization
Method to solve optimization problems
programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject
Linear_programming
Competitive algorithm for searching a problem space
algorithms are commonly used to generate high-quality solutions to optimization and search problems via biologically inspired operators such as selection, crossover
Genetic_algorithm
Optimization problem
Job-shop scheduling, the job-shop problem (JSP) or job-shop scheduling problem (JSSP) is an optimization problem in computer science and operations research
Job-shop_scheduling
Generalization of linear programming
the study of algorithms, an LP-type problem (also called a generalized linear program) is an optimization problem that shares certain properties with
LP-type_problem
Class of algorithms that find approximate solutions to optimization problems
efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the
Approximation_algorithm
Branch of mathematics
{\displaystyle g_{i}(x)\geqslant 0,i=1,\ldots ,r} . Global optimization is distinguished from local optimization by its focus on finding the minimum or maximum over
Global_optimization
consumption. For another optimization, the inputs could be business choices and the output could be the profit obtained. An optimization problem, (in this case
List_of_optimization_software
Optimization problem
The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a
Vehicle_routing_problem
Combinatorial optimization problem
The activity selection problem is a combinatorial optimization problem concerning the selection of non-conflicting activities to perform within a given
Activity_selection_problem
Combinatorial optimization problem
quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research
Quadratic_assignment_problem
Mathematical optimization problem restricted to integers
An integer programming, also known as integer optimization, problem is a mathematical optimization or feasibility program in which some or all of the variables
Integer_programming
Compiler that optimizes generated code
code optimized for some aspect. Optimization is limited by a number of factors. Theoretical analysis indicates that some optimization problems are NP-complete
Optimizing_compiler
Cost-minimizing level of an input in economics
mathematical formulation of this problem, two inputs are used (often labor and capital), and the optimization problem seeks to minimize the total cost
Conditional_factor_demands
Problem a computer might be able to solve
R(x, y) }|. An optimization problem asks for finding a "best possible" solution among the set of all possible solutions to a search problem. One example
Computational_problem
Computer programming paradigm
solutions of the problem; proving the unsatisfiability of the problem. A constraint optimization problem (COP) is a constraint satisfaction problem associated
Constraint_programming
Combinatorial optimization problem
assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has
Assignment_problem
Type of multi-objective optimization
Lexicographic optimization is a kind of multi-objective optimization. In general, multi-objective optimization deals with optimization problems with two or
Lexicographic_optimization
Condition of an optimization problem which the solution must satisfy
In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily
Constraint_(mathematics)
Optimization algorithm for artificial neural networks
the target output t. Therefore, the problem of mapping inputs to outputs can be reduced to an optimization problem of finding a function that will produce
Backpropagation
Numerical optimization process
A sum-of-squares optimization program is an optimization problem with a linear cost function and constraints that certain polynomials constructed from
Sum-of-squares_optimization
2012 American film
problem, one of the most challenging mathematical problems in history. The title refers to the travelling salesman problem, an optimization problem that
Travelling Salesman (2012 film)
Travelling_Salesman_(2012_film)
Set of all Pareto efficient situations
means when there are many distinct objectives to consider in an optimization problem, a Pareto front represents the set of solutions where no solution
Pareto_frontier
Optimization problem in mathematics
In mathematical optimization, a quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and
Quadratically constrained quadratic program
Quadratically_constrained_quadratic_program
Concept in mathematical optimization
this problem had been stated in an unpublished master's thesis by William Karush in 1939. Consider the following nonlinear optimization problem in standard
Karush–Kuhn–Tucker_conditions
Process of finding the optimal set of variables for a machine learning algorithm
In machine learning, hyperparameter optimization or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter
Hyperparameter_optimization
Numerical method
towards its parameters in a constraint optimization form. By using the dual form of this constraint optimization problem, it can be used to calculate the gradient
Adjoint_state_method
Branch of mathematical optimization
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization, some or all of the
Discrete_optimization
Study of optimal transportation and allocation of resources
_{j=1}^{J}\psi _{j}\nu _{j}\right\}} which is a finite-dimensional convex optimization problem that can be solved by standard techniques, such as gradient descent
Transportation theory (mathematics)
Transportation_theory_(mathematics)
Computer networking optimization problem
The C10k problem was the problem of optimizing computer networking stacks to handle a large number of clients at the same time. The name C10k is a numeronym
C10k_problem
Mathematical and computational problem
The bin packing problem is an optimization problem, in which items of different sizes must be packed into a finite number of bins or containers, each of
Bin_packing_problem
Finding shortest walks through all graph edges
theory and combinatorial optimization, Guan's route problem, the Chinese postman problem, postman tour or route inspection problem is to find a shortest
Chinese_postman_problem
Design of highway systems to maximize utility
network optimization is the problem of configuring highway networks to maximize economic and social utility. Numerous mathematical optimization techniques
Highway_network_optimization
Mathematical optimization problem
A min-max optimization (MMO) problem is a mathematical optimization problem of the following form: min x ∈ R d x max y ∈ R d y f ( x , y ) such
Min-max_optimization
Algorithm for solving the quadratic programming problem from training SVMs
Sequential minimal optimization (SMO) is an algorithm for solving the quadratic programming (QP) problem that arises during the training of support-vector
Sequential minimal optimization
Sequential_minimal_optimization
Mathematics of convex functions and sets
Lagrange duality of constrained optimization is a special case of this general principle. For a convex optimization problem minxf0(x)subject tofi(x)≤0,i=1
Convex_analysis
Problem of determining if a Boolean formula could be made true
decision and optimization problems, are at most as difficult to solve as SAT. There is no known algorithm that efficiently solves each SAT problem (where "efficiently"
Boolean satisfiability problem
Boolean_satisfiability_problem
Probabilistic optimization technique and metaheuristic
it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA can
Simulated_annealing
Optimization problem in computer science
Talent scheduling is a combinatorial optimization problem in computer science and operations research. Consider a scenario where multiple films are to
Talent_scheduling
Algorithm for transforming one optimization problem into another
approximation-preserving reduction is an algorithm for transforming one optimization problem into another problem, such that the distance of solutions from optimal is preserved
Approximation-preserving reduction
Approximation-preserving_reduction
Solving an optimization problem with a quadratic objective function
of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate
Quadratic_programming
Vector optimization is a subarea of mathematical optimization where optimization problems with vector-valued objective functions are optimized with respect
Vector_optimization
Online optimization is a field of optimization theory, more popular in computer science and operations research, that deals with optimization problems having
Online_optimization
Process of calculating the causal factors that produced a set of observations
the optimization. Should the objective function be based on a norm other than the Euclidean norm, we have to leave the area of quadratic optimization. As
Inverse_problem
configuration of a physical system with the output being its energy. An optimization problem can be represented in the following way Given: a function f : A →
Comparison of optimization software
Comparison_of_optimization_software
Distributed constraint optimization (DCOP or DisCOP) is the distributed analogue to constraint optimization. A DCOP is a problem in which a group of agents
Distributed constraint optimization
Distributed_constraint_optimization
Optimization problem in computer science
lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability of such problems is central
Lattice_problem
Quantum computing company
single mathematical operation, discrete optimization. Rainier uses quantum annealing to solve optimization problems. The D-Wave One was claimed to be the
D-Wave_Systems
Branch of numerical optimization
Deterministic global optimization is a branch of mathematical optimization which focuses on finding the global solutions of an optimization problem whilst providing
Deterministic global optimization
Deterministic_global_optimization
Topics referred to by the same term
In mathematical optimization and computer science, the set of all possible points of an optimization problem that satisfy the problem's targets or goals
Search_space
Computational geometry and optimization concept
that approximately preserves the value of a specified optimization problem. Solving the problem on the coreset yields a solution whose cost is provably
Coreset
Optimization problem
Optimal job scheduling is a class of optimization problems related to scheduling. The inputs to such problems are a list of jobs (also called processes
Optimal_job_scheduling
Iterative method in numerical analysis
{\displaystyle g(x^{*})={\vec {0}}} . We can therefore rephrase the problem as an optimization problem where we want to minimize ‖ g ( x ) ‖ 2 {\displaystyle \|g(x)\|_{2}}
Anderson_acceleration
Classification of algorithm
cooling schedule, has been proven to find the global optimum of any optimization problem. However, such a cooling schedule results in entirely impractical
Galactic_algorithm
Convex optimization problem
A second-order cone program (SOCP) is a convex optimization problem of the form minimize f T x {\displaystyle \ f^{T}x\ } subject to ‖ A i x + b i
Second-order_cone_programming
Problem in computational complexity theory
WPM1, PM2. MAX-SAT is one of the optimization extensions of the boolean satisfiability problem, which is the problem of determining whether the variables
Maximum satisfiability problem
Maximum_satisfiability_problem
Matrix approximation problem in linear algebra
{\displaystyle B} . Specifically, the orthogonal Procrustes problem is an optimization problem given by minimize Ω ‖ Ω A − B ‖ F subject to Ω T Ω = I , {\displaystyle
Orthogonal_Procrustes_problem
Method for finding stationary points of a function
is relevant in optimization, which aims to find (global) minima of the function f {\displaystyle f} . The central problem of optimization is minimization
Newton's method in optimization
Newton's_method_in_optimization
Classical problem in combinatorics
Karp's 21 NP-complete problems shown to be NP-complete in 1972. The optimization/search version of set cover is NP-hard. It is a problem "whose study has led
Set_cover_problem
Optimization method
Stochastic optimization (SO) are optimization methods that generate and use random variables. For stochastic optimization problems, the objective functions
Stochastic_optimization
Optimization method
multi-objective optimization deals with optimization problems with two or more objective functions to be optimized simultaneously. Lexmaxmin optimization presumes
Lexicographic max-min optimization
Lexicographic_max-min_optimization
Problem optimization method
a relation between the value of the larger problem and the values of the sub-problems. In the optimization literature, this relationship is called the
Dynamic_programming
Subfield of convex optimization
Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine
Conic_optimization
Type of approximation algorithm
for optimization problems (most often, NP-hard optimization problems). A PTAS is an algorithm which takes an instance of an optimization problem and a
Polynomial-time approximation scheme
Polynomial-time_approximation_scheme
Simulation-based optimization (also known as simply simulation optimization) integrates optimization techniques into simulation modeling and analysis
Simulation-based_optimization
that always solve an optimization problem to optimality. Unless P = NP, an exact algorithm for an NP-hard optimization problem cannot run in worst-case
Exact_algorithm
Method to solve constrained optimization problems
continuous first derivatives). Consider the following constrained optimization problem: maximize f ( x ) subject to: g ( x ) = 0 {\displaystyle
Lagrange_multiplier
Problem of finding the optimal shape under given conditions
Shape optimization is part of the field of optimal control theory. The typical problem is to find the shape which is optimal in that it minimizes a certain
Shape_optimization
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OPTIMIZATION PROBLEM
OPTIMIZATION PROBLEM
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OPTIMIZATION PROBLEM
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OPTIMIZATION PROBLEM
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OPTIMIZATION PROBLEM
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