"Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives."
The study of maximizing or minimizing a function subject to constraints.
Linear Programming: A mathematical approach to determine the best solution to a problem where the constraints and the objective function are linear.
Nonlinear Programming: A mathematical approach to determine the best solution to a problem where the constraints and the objective function are nonlinear.
Convex Optimization: A mathematical approach to determine the best solution to a problem where the objective function is a convex function and the constraints are convex sets.
Stochastic Optimization: A mathematical approach to determine the best solution to a problem where some of the parameters are uncertain, and the objective function includes a probabilistic component.
Integer Programming: A mathematical approach to determine the best solution to a problem where some or all of the variables are restricted to integer values.
Combinatorial Optimization: A mathematical approach to determine the best solution to a discrete problem where a set of feasible solutions have to be explored to determine the optimal one.
Global Optimization: A mathematical approach to determine the best solution to a problem where the objective function may have multiple local optima, and the search for the global optimum requires special techniques.
Multi-Objective Optimization: A mathematical approach to determine the best solution to a problem where there are multiple objectives to be optimized, and where the trade-offs between them are not always clear.
Sensitivity Analysis: A mathematical approach to determine the effects of changes in the parameters of a function on the optimal solution.
Numerical Optimization: A mathematical approach to determine the best solution to a problem where the objective function cannot be solved analytically, and numerical methods have to be used.
Real-Time Optimization: A mathematical approach to determine the best solution to a problem in real-time, where the available time to compute the optimal solution is limited.
Robust Optimization: A mathematical approach to determine the best solution to a problem where the parameters are uncertain, and the optimal solution has to be robust to variations in these parameters.
Metaheuristics: A set of optimization techniques that are used to solve difficult optimization problems, where traditional optimization methods are not effective.
Heuristics: A set of optimization techniques that use approximations and rules of thumb to find good solutions to optimization problems.
Optimization Software: A set of computer programs that implement different optimization techniques to solve different types of optimization problems.
Linear programming: Involves optimizing a linear objective function subject to linear constraints.
Nonlinear programming: Involves optimizing a nonlinear objective function subject to nonlinear constraints.
global optimization: Involves finding the global minimum or maximum of a nonlinear objective function that may have multiple local minima or maxima.
Integer programming: Involves optimizing an objective function subject to integer constraints, where the decision variables are required to take integer values.
Network optimization: Involves optimizing the flow of resources or information through a network, such as a transportation system, communication network, or supply chain.
Multi-objective optimization: Involves optimizing multiple conflicting objectives simultaneously, where no single solution can give the best results for all objectives.
Stochastic optimization: Involves optimizing an objective function that involves random or uncertain variables.
Dynamic optimization: Involves optimizing over time, by considering a sequence of decisions that affect future outcomes.
Convex optimization: Involves optimizing a convex objective function subject to convex constraints, where a global solution can be found efficiently.
Robust optimization: Involves optimizing an objective function that is resistant to uncertainties or modeling errors.
Constraint optimization: Involves optimizing a function subject to one or more constraints, where the feasible space is defined by the constraints.
Black box optimization: Involves optimizing an objective function that is not explicitly formulated, but is evaluated through a simulation or experiment.
Mixed-integer nonlinear programming (MINLP): Involves optimizing an objective function subject to both nonlinear and integer constraints.
Topology optimization: Involves optimizing the material layout or design of a structure to optimize its performance under given load conditions.
"It is generally divided into two subfields: discrete optimization and continuous optimization."
"Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics."
"The development of solution methods has been of interest in mathematics for centuries."
"In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function."
"The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics."
"Optimization includes finding 'best available' values of some objective function given a defined domain (or input)."
"Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics."
"Mathematical optimization (alternatively spelled optimisation)..."
"It is generally divided into two subfields: discrete optimization and continuous optimization."
"The development of solution methods has been of interest in mathematics for centuries."
"The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics."
"It is generally divided into two subfields: discrete optimization and continuous optimization."
"The selection of a best element, with regard to some criterion, from some set of available alternatives."
"Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics."
"The development of solution methods has been of interest in mathematics for centuries."
"The generalization of optimization theory and techniques..."
"Optimization includes finding 'best available' values of some objective function given a defined domain (or input)."
"The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics."
"Mathematical optimization (alternatively spelled optimisation)..."