Quadratic Programming and Cone Programming

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.


expand all

evaluateEvaluate optimization expression
infeasibilityConstraint violation at a point
optimproblemCreate optimization problem
optimvarCreate optimization variables
solveSolve optimization problem or equation problem
coneprogSecond-order cone programming solver
quadprogQuadratic programming
secondorderconeCreate second-order cone constraint

Live Editor Tasks

OptimizeOptimize or solve equations in the Live Editor


SecondOrderConeConstraintSecond-order cone constraint object


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.

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.

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.

Second-Order Cone Programming

Minimize Energy of Piecewise Linear Mass-Spring System Using Cone Programming

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.

Optimization Code Generation for Real-Time Applications

Explore techniques for handling real-time requirements in generated code.

Problem-Based Algorithms

Problem-Based Optimization Algorithms

How the optimization functions and objects solve optimization problems.

Supported Operations on Optimization Variables and Expressions

Lists all available mathematical and indexing operations on 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.