Quadratic Programming and Cone Programming - MATLAB & Simulink (original) (raw)

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Solve problems with quadratic objectives and linear constraints or with conic constraints

Before you begin to solve an optimization problem, you must choose the appropriate approach: problem-based or solver-based. For details, see First Choose Problem-Based or Solver-Based Approach.

For the problem-based approach, create problem variables, and then represent the objective function and constraints in terms of these symbolic variables. For the problem-based steps to take, see Problem-Based Optimization Workflow. To solve the resulting problem, use solve.

For the solver-based steps to take, including defining the objective function and constraints, and choosing the appropriate solver, see Solver-Based Optimization Problem Setup. To solve the resulting problem, use quadprog or coneprog.

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Topics

Problem-Based Quadratic Programming

• Quadratic Programming with Bound Constraints: Problem-Based
  Shows how to solve a problem-based quadratic programming problem with bound constraints using different algorithms.
• Large Sparse Quadratic Program, Problem-Based
  Shows how to solve a large sparse quadratic program using the problem-based approach.
• Bound-Constrained Quadratic Programming, Problem-Based
  Example showing large-scale problem-based quadratic programming.
• Quadratic Programming for Portfolio Optimization, Problem-Based
  Example showing problem-based quadratic programming on a basic portfolio model.
• Diversify Portfolios Using Optimization Toolbox
  This example shows three techniques of asset diversification in a portfolio using optimization functions.

Solver-Based Quadratic Programming

• Quadratic Minimization with Bound Constraints
  Example of quadratic programming with bound constraints and various options.
• Quadratic Programming with Many Linear Constraints
  This example shows the benefit of the active-set algorithm on problems with many linear constraints.
• Warm Start quadprog
  Shows that warm start can be effective in a large quadratic program.
• Warm Start Best Practices
  Describes how best to use warm start for speeding repeated solutions.
• Quadratic Minimization with Dense, Structured Hessian
  Example showing how to save memory in a structured quadratic program.
• Large Sparse Quadratic Program with Interior Point Algorithm
  Example showing how to save memory in a quadratic program by using a sparse quadratic matrix.
• Bound-Constrained Quadratic Programming, Solver-Based
  Example showing solver-based large-scale quadratic programming.
• Quadratic Programming for Portfolio Optimization Problems, Solver-Based
  Example showing solver-based quadratic programming on a basic portfolio model.

Problem-Based Second-Order Cone Programming

• Minimize Energy of Piecewise Linear Mass-Spring System Using Cone Programming, Problem-Based
  Presents a problem-based example of cone programming.
• Discretized Optimal Trajectory, Problem-Based
  This example shows how to solve a discretized optimal trajectory problem using the problem-based approach.
• Compare Speeds of coneprog Algorithms
  This section gives timing information for a sequence of cone programming problems using various LinearSolver option settings.
• Write Constraints for Problem-Based Cone Programming
  Requirements for solve to use coneprog for problem solution.

Solver-Based Second-Order Cone Programming

• Minimize Energy of Piecewise Linear Mass-Spring System Using Cone Programming, Solver-Based
  Solve a mechanical mass-spring problem using cone programming.
• Convert Quadratic Constraints to Second-Order Cone Constraints
  Convert quadratic constraints into coneprog form.
• Convert Quadratic Programming Problem to Second-Order Cone Program
  Convert a quadratic programming problem to a second-order cone problem.

Code Generation

• Code Generation for quadprog Background
  Prerequisites to generate C code for quadratic optimization.
• Generate Code for quadprog
  Learn the basics of code generation for the quadprog optimization solver.
• Generate Single-Precision quadprog Code
  Generate single-precision code for quadratic programming problems.
• Code Generation for coneprog Background
  Prerequisites to generate C code for cone programming.
• Generate Code for coneprog
  Provides an example of code generation inconeprog.
• Warm Start Best Practices
  Describes how best to use warm start for speeding repeated solutions.
• Optimization Code Generation for Real-Time Applications
  Explore techniques for handling real-time requirements in generated code.

Problem-Based Algorithms

• Problem-Based Optimization Algorithms
  Learn how the optimization functions and objects solve optimization problems.
• Write Constraints for Problem-Based Cone Programming
  Requirements for solve to use coneprog for problem solution.
• Supported Operations for Optimization Variables and Expressions
  Explore the supported mathematical and indexing operations for optimization variables and expressions.

Algorithms and Options

• Quadratic Programming Algorithms
  Minimizing a quadratic objective function in n dimensions with only linear and bound constraints.
• Second-Order Cone Programming Algorithm
  Description of the underlying algorithm.
• Optimization Options Reference
  Explore optimization options.