Month: November 2002

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

    Quadratic Convergence of a Squared Smoothing Newton Method for Nonsmooth Matrix Equations and Its Applications in Semidefinite Optimization Problems

  • Liqun Qi
  • Jie Sun
  • Defeng Sun
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization, Semi-definite Programming Tags ,

    We study a smoothing Newton method for solving a nonsmooth matrix equation that includes semidefinite programming and the semidefinte complementarity problem as special cases. This method, if specialized for solving semidefinite programs, needs to solve only one linear system per iteration and achieves quadratic convergence under strict complementarity. We also establish quadratic convergence of this … Read more

    A unifying framework for several cutting plane algorithms for semidefinite programming

  • Kartik Krishnan
  • John E. Mitchell
    • Categories Nonsmooth Optimization, Semi-definite Programming, Semi-infinite Programming Tags , , ,

    Cutting plane methods provide the means to solve large scale semidefinite programs (SDP) cheaply and quickly. They can also conceivably be employed for the purposes of re-optimization after branching, or the addition of cutting planes. We give a survey of various cutting plane approaches for SDP in this paper. These cutting plane approaches arise from … Read more

    New Variable Metric Methods for Unconstrained Minimization Covering the Large-Scale Case

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    A new family of numerically efficient variable metric or quasi-Newton methods for unconstrained minimization are given, which give simple possibility of adaptation for large-scale optimization. Global convergence of the methods can be established for convex sufficiently smooth functions. Some encouraging numerical experience is reported. Citation Report V876, Institute of Computer Science, AV CR, Pod Vodarenskou … Read more

    Nonsmooth Equation Method for Nonlinear Nonconvex Optimization

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags ,

    In this paper, we propose an algorithm for solving nonlinear nonconvex programming problems, which is based on the nonsmooth equation approach. This Algorithm was implemented in the interactive system for universal functional optimization UFO. Results of numerical experiments are reported. Citation Report V844, Institute of Computer Science, AV CR, Pod Vodarenskou Vezi 2, 18207 Praha … Read more

    Interior-Point Method for Nonlinear Nonconvex Optimization

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags ,

    In this paper, we propose an algorithm for solving nonlinear nonconvex programming problems, which is based on the interior-point approach. Main theoretical results concern direction determination and step-length selection. We split inequality constraints into active and inactive to overcome problems with stability. Inactive constraints are eliminated directly while active constraints are used to define symmetric … Read more

    RIOTS_95–a MATLAB Toolbox for Solving General Optimal Control Problems And Its Applications to Chemical Processes

  • YangQuan Chen
  • Adam L. Schwartz
    • Categories Chemical Engineering, Problem Solving Environments, Systems governed by Differential Equations Optimization Tags , , , , ,

    RIOTS_95 is a group of programs and utilities, written mostly in C, Fortran and M-file scripts and designed as a toolbox for MATLAB, that provides an interactive environment for solving a very broad class of optimal control problems (OCP’s). RIOTS_95 comes pre-compiled for use with the Windows 95/98/2000 or Windows NT operating systems. The user’s … Read more

    Domination Analysis of Combinatorial Optimization Problems.

  • Gregory Gutin
  • Anders Yeo
  • Alek Vainshtein
    • Categories Approximation Algorithms, Combinatorial Optimization

    We use the notion of domination ratio introduced by Glover and Punnen in 1997 to present a new classification of combinatorial optimization (CO) problems: $\DOM$-easy and $\DOM$-hard problems. It follows from results proved already in the 1970’s that {\tt min TSP} (both symmetric and asymmetric versions) is $\DOM$-easy. We prove that several CO problems are … Read more

    Nonlinear Optimisation in CHP-Applications

  • Wilhelm Althaus
  • Michael Lucht
  • Michael Wigbels
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    At the Fraunhofer Institute UMSICHT a nonlinear model has been developed facilitating the dynamic optimisation of combined heat and power production systems. The strategy called “dynamic supply temperature optimisation” is a very promising approach to use the DH-network itself as a large heat storage causing no additional investment cost. The pipeline system of a district … Read more