Documentation

Create an optimization problem object by using optimproblem. A problem object is a container in which you define an objective expression and constraints. The optimization problem object defines the problem and any bounds that exist in the problem variables.

For example, create a maximization problem.

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

Create named variables by using optimvar. An optimization variable is a symbolic variable that you use to describe the problem objective and constraints. Include any bounds in the variable definitions.

For example, create a 15-by-3 array of binary variables named 'x'.

x = optimvar('x',15,3,'Type','integer','LowerBound',0,'UpperBound',1);

Define the objective function in the problem object as an expression in the named variables.

If necessary, include extra parameters in your expression as workspace variables; see Pass Extra Parameters in Problem-Based Approach.

For example, assume that you have a real matrix f of the same size as a matrix of variables x, and the objective is the sum of the entries in f times the corresponding variables x.

prob.Objective = sum(sum(f.*x));

Define constraints for optimization problems as either comparisons in the named variables or as comparisons of expressions.

For example, assume that the sum of the variables in each row of x must be one, and the sum of the variables in each column must be no more than one.

onesum = sum(x,2) == 1;
vertsum = sum(x,1) <= 1;
prob.Constraints.onesum = onesum;
prob.Constraints.vertsum = vertsum;

For nonlinear problems, set an initial point as a structure whose fields are the optimization variable names. For example:

x0.x = randn(size(x));
x0.y = eye(4); % Assumes y is a 4-by-4 variable

Solve the problem by using solve.

sol = solve(prob);
% Or, for nonlinear problems,
sol = solve(prob,x0)