Choose MINLP Solvers for Portfolio Problems

The following sections list the type of Mixed Integer Nonlinear Programming (MINLP) solvers that you can select to find the solution to different portfolio problems using a Portfolio, PortfolioCVaR, or PortfolioMAD object. You can set the solvers using setSolverMINLP, where the first input argument, solverTypeMINLP, is one of the solvers listed in the tables that follow.

Problems with Cardinality Constraints and/or Conditional Bounds Without Tracking Error Constraints

When solving a mixed-integer problem that uses a Portfolio, PortfolioCVaR, or PortfolioMAD object with cardinality constraints (see setMinMaxNumAssets) and/or conditional bounds (see setBounds), but without tracking error constraints (see setTrackingError), use these solvers with setSolverMINLP:

		Available Solvers (Use setSolverMINLP to specify the solver)
Portfolio Problem	Use Function:	Portfolio Object	PortfolioCVaR Object	PortfolioMAD Object
Estimate efficient frontier	estimateFrontier(p) (See estimateFrontier)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	ExtendedCP OuterApproximation TrustRegionCP (default)	ExtendedCP OuterApproximation TrustRegionCP (default)
Minimize risk without return constraint	estimateFrontierLimits(p,'min') (See estimateFrontierLimits)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	ExtendedCP OuterApproximation TrustRegionCP (default)	ExtendedCP OuterApproximation TrustRegionCP (default)
Maximize return without risk constraint	estimateFrontierLimits(p,'max') (See estimateFrontierLimits)	intlinprog Use IntMainSolverOptions name-value argument to control intlinprog options.	intlinprog Use IntMainSolverOptions name-value argument to control intlinprog options.	intlinprog Use IntMainSolverOptions name-value argument to control intlinprog options.
Minimize risk subject to a return constraint	estimateFrontierByReturn(p,returnTarget) (See estimateFrontierByReturn)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	ExtendedCP OuterApproximation TrustRegionCP (default)	ExtendedCP OuterApproximation TrustRegionCP (default)
Maximize return subject to a risk constraint	estimateFrontierByRisk(p,riskTarget) (See estimateFrontierByRisk)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	ExtendedCP OuterApproximation TrustRegionCP (default)	ExtendedCP OuterApproximation TrustRegionCP (default)
Maximize Sharpe ratio	estimateMaxSharpeRatio(p) (See estimateMaxSharpeRatio)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	ExtendedCP OuterApproximation TrustRegionCP (default)	ExtendedCP OuterApproximation TrustRegionCP (default)
Optimize custom linear objective	estimateCustomObjectivePortfolio(p,linFun) (See estimateCustomObjectivePortfolio)	intlinprog Use IntMainSolverOptions name-value argument to control intlinprog options.	Not supported	Not supported
Optimize custom quadratic objective	estimateCustomObjectivePortfolio(p,quadFun) (See estimateCustomObjectivePortfolio)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	Not supported	Not supported
Optimize custom nonlinear nonquadratic objective	estimateCustomObjectivePortfolio(p,NLFun) (See estimateCustomObjectivePortfolio)	ExtendedCP OuterApproximation (default) TrustRegionCP	Not supported	Not supported

Problems with Cardinality Constraints and/or Conditional Bounds With Tracking Error Constraints

When solving a mixed-integer problem that uses a Portfolio, PortfolioCVaR, or PortfolioMAD object with cardinality constraints (see setMinMaxNumAssets) and/or conditional bounds (see setBounds), and with tracking error constraints (see setTrackingError), use these solvers with setSolverMINLP:

		Available Solvers (Use setSolverMINLP to specify the solver)
Portfolio Problem	Use Function:	Portfolio Object	PortfolioCVaR Object	PortfolioMAD Object
Estimate efficient frontier	estimateFrontier(p) (See estimateFrontier)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	ExtendedCP OuterApproximation TrustRegionCP (default)	ExtendedCP OuterApproximation TrustRegionCP (default)
Minimize risk without return constraint	estimateFrontierLimits(p,'min') (See estimateFrontierLimits)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	ExtendedCP OuterApproximation TrustRegionCP (default)	ExtendedCP OuterApproximation TrustRegionCP (default)
Maximize return without risk constraint	estimateFrontierLimits(p,'max') (See estimateFrontierLimits)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	ExtendedCP OuterApproximation TrustRegionCP (default)	ExtendedCP OuterApproximation TrustRegionCP (default)
Minimize risk subject to a return constraint	estimateFrontierByReturn(p,returnTarget) (See estimateFrontierByReturn)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	ExtendedCP OuterApproximation TrustRegionCP (default)	ExtendedCP OuterApproximation TrustRegionCP (default)
Maximize return subject to a risk constraint	estimateFrontierByRisk(p,riskTarget) (See estimateFrontierByRisk)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	ExtendedCP OuterApproximation TrustRegionCP (default)	ExtendedCP OuterApproximation TrustRegionCP (default)
Maximize Sharpe ratio	estimateMaxSharpeRatio(p) (See estimateMaxSharpeRatio)	ExtendedCP OuterApproximation (default) Supports extended formulation using the name-value argument ExtendedFormulation. TrustRegionCP	ExtendedCP OuterApproximation TrustRegionCP (default)	ExtendedCP OuterApproximation TrustRegionCP (default)
Optimize custom objective	estimateCustomObjectivePortfolio(p,linFun) (See estimateCustomObjectivePortfolio)	Not supported	Not supported	Not supported