Using 'lcprog' and 'quadprog'

To modify either lcprog or to specify quadprog as your solver, use the setSolver function to set the hidden properties solverType and solverOptions that specify and control the solver. Because the solver properties are hidden, you cannot set these options using the Portfolio object. The default solver is lcprog so you do not need to use setSolver to specify this solver. To use quadprog, you can set the default interior-point-convex algorithm of quadprog using this code:

p = Portfolio;
p = setSolver(p, 'quadprog');
display(p.solverType)
display(p.solverOptions)

quadprog options:

   Options used by current Algorithm ('interior-point-convex'):
   (Other available algorithms: 'active-set', 'trust-region-reflective')

   Set properties:
              Algorithm: 'interior-point-convex'
                Display: 'off'
    OptimalityTolerance: 1.0000e-12

   Default properties:
    ConstraintTolerance: 1.0000e-08
           LinearSolver: 'auto'
          MaxIterations: 200
          StepTolerance: 1.0000e-12

p = setSolver(p, 'lcprog');
display(p.solverType);
display(p.solverOptions)

lcprog
     MaxIter: []
    TieBreak: []
      TolPiv: 5.0000e-08

p = Portfolio;
p = setSolver(p, 'quadprog', 'Algorithm', 'trust-region-reflective');
display(p.solverOptions)

  quadprog options:

   Options used by current Algorithm ('trust-region-reflective'):
   (Other available algorithms: 'active-set', 'interior-point-convex')

   Set properties:
              Algorithm: 'trust-region-reflective'

   Default properties:
                Display: 'final'
      FunctionTolerance: 'default dependent on problem'
     HessianMultiplyFcn: []
          MaxIterations: 'default dependent on problem'
    OptimalityTolerance: 'default dependent on problem'
          StepTolerance: 2.2204e-14
    SubproblemAlgorithm: 'cg'
               TypicalX: 'ones(numberOfVariables,1)'

In addition, if you want to specify any of the options for quadprog that you typically set through optimoptions from Optimization Toolbox, setSolver accepts an optimoptions object as the second argument. For example, you can start with the default options for quadprog set by setSolver and then change the algorithm to 'trust-region-reflective' with no displayed output:

p = Portfolio;
options = optimoptions('quadprog', 'Algorithm', 'trust-region-reflective', 'Display', 'off');
p = setSolver(p, 'quadprog', options);
display(p.solverOptions.Algorithm)
display(p.solverOptions.Display)

trust-region-reflective
off

Using the Mixed Integer Nonlinear Programming (MINLP) Solver

The mixed integer nonlinear programming (MINLP) solver, configured using setSolverMINLP, enables you to specify associated solver options for portfolio optimization for a Portfolio object. The MINLP solver is used when any one, or any combination of 'Conditional' BoundType, MinNumAssets, or MaxNumAssets constraints are active. In this case, you formulate the portfolio problem by adding NumAssets binary variables, where 0 indicates not invested, and 1 is invested. For more information on using 'Conditional' BoundType, see setBounds. For more information on specifying MinNumAssets and MaxNumAssets, see setMinMaxNumAssets.

When using the estimate functions with a Portfolio object where 'Conditional' BoundType, MinNumAssets, or MaxNumAssets constraints are active, the mixed integer nonlinear programming (MINLP) solver is automatically used.

Solver Guidelines for Portfolio Objects

The following table provides guidelines for using setSolver and setSolverMINLP.

Solver Guidelines for Custom Objective Problems Using Portfolio Objects

The following table provides guidelines for using setSolver and setSolverMINLP when using estimateCustomObjectivePortfolio.