# OptimizationProblem

Optimization problem

## Description

An OptimizationProblem object describes an optimization problem, including variables for the optimization, constraints, the objective function, and whether the objective is to be maximized or minimized. Solve a complete problem using solve.

## Creation

Create an OptimizationProblem object by using optimproblem.

### Warning

The problem-based approach does not support complex values in an objective function, nonlinear equalities, or nonlinear inequalities. If a function calculation has a complex value, even as an intermediate value, the final result can be incorrect.

## Properties

expand all

Problem label, specified as a string or character vector. The software does not use Description. It is an arbitrary label that you can use for any reason. For example, you can share, archive, or present a model or problem, and store descriptive information about the model or problem in the Description property.

Example: "Describes a traveling salesman problem"

Data Types: char | string

Indication to minimize or maximize, specified as 'minimize' or 'maximize'. This property affects how solve works.

You can use the short name 'min' for 'minimize' or 'max' for 'maximize'.

Example: 'maximize'

Data Types: char | string

Optimization variables in the object, specified as a structure of OptimizationVariable objects.

Data Types: struct

Objective function, specified as a scalar OptimizationExpression or as a structure containing a scalar OptimizationExpression. Incorporate an objective function into the problem when you create the problem, or later by using dot notation.

% or
prob = optimproblem;

Optimization constraints, specified as an OptimizationConstraint object, an OptimizationEquality object, an OptimizationInequality object, or as a structure containing one of these objects. Incorporate constraints into the problem when you create the problem, or later by using dot notation:

constrs = struct('TrayArea',10*brownies + 20*cookies <= traysize,...
prob = optimproblem('Constraints',constrs)
% or
prob.Constraints.TrayArea = 10*brownies + 20*cookies <= traysize
prob.Constraints.TrayWeight = 12*brownies + 18*cookies <= maxweight

Remove a constraint by setting it to [].

prob.Constraints.TrayArea = [];

## Object Functions

 optimoptions Create optimization options prob2struct Convert optimization problem or equation problem to solver form show Display information about optimization object solve Solve optimization problem or equation problem varindex Map problem variables to solver-based variable index write Save optimization object description

## Examples

collapse all

Create a linear programming problem for maximization. The problem has two positive variables and three linear inequality constraints.

prob = optimproblem('ObjectiveSense','max');

Create positive variables. Include an objective function in the problem.

x = optimvar('x',2,1,'LowerBound',0);
prob.Objective = x(1) + 2*x(2);

Create linear inequality constraints in the problem.

cons1 = x(1) + 5*x(2) <= 100;
cons2 = x(1) + x(2) <= 40;
cons3 = 2*x(1) + x(2)/2 <= 60;
prob.Constraints.cons1 = cons1;
prob.Constraints.cons2 = cons2;
prob.Constraints.cons3 = cons3;

Review the problem.

show(prob)
OptimizationProblem :

Solve for:
x

maximize :
x(1) + 2*x(2)

subject to cons1:
x(1) + 5*x(2) <= 100

subject to cons2:
x(1) + x(2) <= 40

subject to cons3:
2*x(1) + 0.5*x(2) <= 60

variable bounds:
0 <= x(1)
0 <= x(2)

Solve the problem.

sol = solve(prob);
Solving problem using linprog.

Optimal solution found.
sol.x
ans = 2×1

25.0000
15.0000