Convex optimization qp

  • Is QP convex?

    A QP with a semi-definite Hessian is still convex: It has a bowl shape with a "trough" where many points have the same objective value.
    An optimizer will normally find a point in the "trough" with the best objective function value.
    A QP with an indefinite Hessian has a "saddle" shape -- a non-convex function..

  • What is a QP solver?

    The model predictive controller QP solver converts a linear MPC optimization problem to the general form QP problem.
    M i n x ( 1 2 x ⊺ H x + f ⊺ x ) subject to the linear inequality constraints..

  • What is the QP method?

    Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions.
    Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables..

  • CPLEX solves quadratic programs; that is, a model in which the constraints are linear, but the objective function can contain one or more quadratic terms.
    These problems are also known as QP.
    When such problems are convex, CPLEX normally solves them efficiently in polynomial time.
  • The model predictive controller QP solver converts a linear MPC optimization problem to the general form QP problem.
    M i n x ( 1 2 x ⊺ H x + f ⊺ x ) subject to the linear inequality constraints.
Dec 10, 2017This document briefly describes the quadratic programming (QP) problem, a minimization of a quadratic polynomial on a domain defined by 

What is a convex quadratic problem?

Convex quadratic problems can be formulated as linear complementarity problems

One of the most commonly used methods for solving problems of this type is complementary pivot algorithm (CPA) or Lemke’s method, introduced by Lemke ( 1968 )


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Convex quadratic optimization
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Non-convex quadratic optimization
Infeasible convex quadratic optimization problem
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Convex optimization review
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Efficient convex optimization requires superlinear memory
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