Quadratic Programming

Minimize quadratic functions subject to constraints

Quadratic programming (QP) involves minimizing or maximizing an objective function subject to bounds, linear equality, and inequality constraints. Example problems include portfolio optimization in finance, power generation optimization for electrical utilities, and design optimization in engineering.

Quadratic programming is the mathematical problem of finding a vector x that minimizes a quadratic function:

min x   { 1 2 x T H x + f T x }

Subject to the linear constraints:

A x b (inequality constraint)
A eq x = b eq (equality constraint)
lb x ub (bound constraint)

The following algorithms are commonly used to solve quadratic programming problems:

  • Interior-point-convex: solves convex problems with any combination of constraints
  • Trust-region-reflective: solves bound constrained or linear equality constrained problems
  • Active-set: solves problems with any combination of constraints

For more information about quadratic programming, see Optimization Toolbox.

Examples and How To

Software Reference

See also: Optimization Toolbox, Global Optimization Toolbox, linear programming, nonlinear programming, multiobjective optimization, genetic algorithm, simulated annealing