Optimization

Optimization

Optimization is the process of finding values for one or more variables that minimize or maximize an objective while satisfying any required constraints.

Optimization Problem

An optimization problem consists of decision variables, an objective to minimize or maximize, and any constraints that restrict allowable solutions.

Decision Variable

A decision variable is a quantity whose value MATLAB is allowed to change while searching for an optimal solution.

Objective Function

An objective function is the mathematical expression whose value an optimization algorithm attempts to minimize or maximize.

Optimal Solution

An optimal solution is a set of decision-variable values that produces the best achievable objective value while satisfying the required constraints.

Objective Value

The objective value is the value of the objective function at a particular set of decision-variable values.

Minimization

Minimization is an optimization process that searches for decision-variable values that produce the smallest possible objective value.

Maximization

Maximization is an optimization process that searches for decision-variable values that produce the largest possible objective value.

Constraint

A constraint is a condition that restricts the values that decision variables may take in an optimization problem.

Equality Constraint

An equality constraint requires an expression involving the decision variables to equal a specified value.

Inequality Constraint

An inequality constraint restricts an expression using an inequality such as less than or equal to or greater than or equal to.

Bound Constraint

A bound constraint specifies a lower bound, upper bound, or both for a decision variable.

Constrained Optimization

Constrained optimization searches for an optimal solution while requiring the decision variables to satisfy specified constraints.

Unconstrained Optimization

Unconstrained optimization searches for an optimal solution without explicit restrictions on the allowable decision-variable values.

Feasible Solution

A feasible solution is a set of decision-variable values that satisfies all constraints of an optimization problem.

Feasible Region

The feasible region is the complete set of possible solutions that satisfy all constraints of an optimization problem.

Optimization Solver

An optimization solver is an algorithm or MATLAB function that searches for a solution to an optimization problem.

fminbnd

fminbnd is a MATLAB function that finds a local minimum of a single-variable function within a specified bounded interval.

fminsearch

fminsearch is a MATLAB function that searches for a local minimum of an unconstrained multivariable objective function without requiring derivatives.

fmincon

fmincon is a MATLAB solver for finding a local minimum of a constrained nonlinear multivariable objective function.

Local Minimum

A local minimum is a solution whose objective value is lower than that of nearby feasible solutions but is not necessarily the lowest value over the entire feasible region.

Global Minimum

A global minimum is a solution having the lowest objective value among all feasible solutions in the entire optimization problem.

Initial Point

An initial point is the starting set of decision-variable values supplied to an optimization solver before its search begins.

Solver Options

Solver options are settings used to control the behavior of an optimization algorithm, such as stopping criteria, tolerances, and displayed output.

optimoptions

optimoptions creates or modifies an options object used to configure supported MATLAB optimization solvers.