quadratic programming

Gradient Projection Methods for Quadratic Programs and Applications in Training Support Vector Machines

  • Thomas Serafini
  • Luca Zanni
  • Gaetano Zanghirati
    • Categories Data-Mining, Quadratic Programming Tags , , , ,

    Gradient projection methods based on the Barzilai-Borwein spectral steplength choices are considered for quadratic programming problems with simple constraints. Well known nonmonotone spectral projected gradient methods and variable projection methods are discussed. For both approaches the behavior of different combinations of the two spectral steplengths is investigated. A nw adaptive stplength alternating rule is proposed, … Read more

    A semidefinite programming heuristic for quadratic programming problems with complementarity constraints

  • Stephen E. Braun
  • John E. Mitchell
    • Categories Complementarity and Variational Inequalities, Finance and Economics, Semi-definite Programming Tags , ,

    The presence of complementarity constraints brings a combinatorial flavour to an optimization problem. A quadratic programming problem with complementarity constraints can be relaxed to give a semidefinite programming problem. The solution to this relaxation can be used to generate feasible solutions to the complementarity constraints. A quadratic programming problem is solved for each of these … Read more

    Rebalancing an Investment Portfolio in the Presence of Transaction Costs

  • Stephen E. Braun
  • John E. Mitchell
    • Categories Finance and Economics, Quadratic Programming Tags , , ,

    The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we consider an extension of the standard portfolio problem in which transaction costs are incurred to rebalance an investment portfolio. The Markowitz framework of mean-variance efficiency is used with costs modelled as a percentage of the value transacted. … Read more

    Lagrangian Smoothing Heuristic for Max-Cut

  • Hernán Alperin
  • Ivo Nowak
    • Categories Combinatorial Optimization Tags , , , , , ,

    This paper presents smoothing heuristics for an NP-hard combinatorial problem based on Lagrangian relaxation. We formulate the Lagrangian dual for this nonconvex quadratic problem and propose eigenvalue nonsmooth unconstrained optimization to solve the dual problem with bundle or subgradient methods. Derived heuristics are considered to obtain good primal solutions through pathfollowing methods using a projected … Read more

    A General Framework for Convex Relaxation of Polynomial Optimization Problems over Cones

  • Sunyoung Kim
  • Masakazu Kojima
  • Hayato Waki
    • Categories Global Optimization, Linear, Cone and Semidefinite Programming Tags , , , , , , ,

    The class of POPs (Polynomial Optimization Problems) over cones covers a wide range of optimization problems such as $0$-$1$ integer linear and quadratic programs, nonconvex quadratic programs and bilinear matrix inequalities. This paper presents a new framework for convex relaxation of POPs over cones in terms of linear optimization problems over cones. It provides a … Read more

    A New Trust Region Technique for the Maximum Weight Clique Problem

  • Stanislav Busygin
    • Categories Approximation Algorithms, Graphs and Matroids Tags , , , , , ,

    A new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a new trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of … Read more

    A Quadratic Programming Bibliography

  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Quadratic Programming Tags ,

    The following is a list of all of the published and unpublished works on quadratic programming that we are aware of. Some are general references to background material, while others are central to the development of the quadratic programming methods and to the applications we intend to cover in our evolving book on the subject. … Read more