Month: April 2009

A continuation method for nonlinear complementarity problems over symmetric cone

  • Chek Beng Chua
  • Peng Yi
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    In this paper, we introduce a new P-type condition for nonlinear functions defined over Euclidean Jordan algebras, and study a continuation method for nonlinear complementarity problems over symmetric cones. This new P-type condition represents a new class of nonmonotone nonlinear complementarity problems that can be solved numerically. CitationResearch Report, Division of Mathematical Sciences, School of … Read more

    Switching stepsize strategies for PDIP

  • Berc Rustem
  • George Tzallas-Regas
    • Categories Constrained Nonlinear Optimization Tags , , , , , ,

    In this chapter we present a primal-dual interior point algorithm for solving constrained nonlinear programming problems. Switching rules are implemented that aim at exploiting the merits and avoiding the drawbacks of three different merit functions. The penalty parameter is determined using an adaptive penalty strategy that ensures a descent property for the merit function. The … Read more

    A Linearly Convergent Linear-Time First-Order Algorithm for Support Vector Classification with a Core Set Result

  • Piyush Kumar
  • E. Alper Yildirim
    • Categories Convex Optimization Tags , , , , ,

    We present a simple, first-order approximation algorithm for the support vector classification problem. Given a pair of linearly separable data sets and $\epsilon \in (0,1)$, the proposed algorithm computes a separating hyperplane whose margin is within a factor of $(1-\epsilon)$ of that of the maximum-margin separating hyperplane. We discuss how our algorithm can be extended … Read more

    Optimal placement of communications relay nodes

  • Oleg Burdakov
  • Patrick Doherty
  • Kaj Holmberg
  • Per-Magnus Olsson
    • Categories Global Optimization, Network Optimization, Telecommunications

    We consider a constrained optimization problem with mixed integer and real variables. It models optimal placement of communications relay nodes in the presence of obstacles. This problem is widely encountered, for instance, in robotics, where it is required to survey some target located in one point and convey the gathered information back to a base … Read more

    A Derivative-Free Algorithm for the Least-square minimization

  • Andrew R. Conn
  • Katya Scheinberg
  • Hongchao Zhang
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , , , ,

    We develop a framework for a class of derivative-free algorithms for the least-squares minimization problem. These algorithms are based on polynomial interpolation models and are designed to take advantages of the problem structure. Under suitable conditions, we establish the global convergence and local quadratic convergence properties of these algorithms. Promising numerical results indicate the algorithm … Read more

    TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalities

  • Benedetta Morini
  • Margherita Porcelli
    • Categories Bound-constrained Optimization, Nonlinear Optimization, Nonlinear Systems and Least-Squares

    The Matlab implementation of a trust-region Gauss-Newton method for bound-constrained nonlinear least-squares problems is presented. The solver, called TRESNEI, is adequate for zero and small-residual problems and handles the solution of nonlinear systems of equalities and inequalities. The structure and the usage of the solver are described and an extensive numerical comparison with functions from … Read more

    A Redistributed Proximal Bundle Method for Nonconvex Optimization

  • Warren Hare
  • Claudia Sagastizábal
    • Categories Generalized Convexity/Monoticity, Nonsmooth Optimization Tags , , , , ,

    Proximal bundle methods have been shown to be highly successful optimization methods for unconstrained convex problems with discontinuous first derivatives. This naturally leads to the question of whether proximal variants of bundle methods can be extended to a nonconvex setting. This work proposes an approach based on generating cutting-planes models, not of the objective function … Read more