Month: February 2015

An Adaptive Unified Differential Evolution Algorithm for Global Optimization

  • Chad Mitchell
  • Ji Qiang
    • Categories Global Optimization, Stochastic Approaches Tags ,

    In this paper, we propose a new adaptive unified differential evolution algorithm for single-objective global optimization. Instead of the multiple mutation strategies proposed in conventional differential evolution algorithms, this algorithm employs a single equation unifying multiple strategies into one expression. It has the virtue of mathematical simplicity and also provides users the flexibility for broader … Read more

    Copositivity for second-order optimality conditions in general smooth optimization problems

  • Immanuel M. Bomze
    • Categories Constrained Nonlinear Optimization, Quadratic Programming Tags , , , ,

    Second-order local optimality conditions involving copositivity of the Hessian of the Lagrangian on the reduced linearization cone have the advantage that there is only a small gap between sufficient (the Hessian is strictly copositive) and necessary (the Hessian is copositive) conditions. In this respect, this is a proper generalization of convexity of the Lagrangian. We … Read more

    On the application of the spectral projected gradient method in image segmentation

  • Laura Antonelli
  • Valentina De Simone
  • Daniela di Serafino
    • Categories Applications - Science and Engineering, Bound-constrained Optimization Tags , ,

    We investigate the application of the nonmonotone spectral projected gradient (SPG) method to a region-based variational model for image segmentation. We consider a “discretize-then-optimize” approach and solve the resulting nonlinear optimization problem by an alternating minimization procedure that exploits the SPG2 algorithm by Birgin, Martì­nez and Raydan (SIAM J. Optim., 10(4), 2000). We provide a … Read more

    A polyhedral study of binary polynomial programs

  • Alberto Del Pia
  • Aida Khajavirad
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Global Optimization

    We study the polyhedral convex hull of a mixed-integer set S defined by a collection of multilinear equations over the 0-1-cube. Such sets appear frequently in the factorable reformulation of mixed-integer nonlinear optimization problems. In particular, the set S represents the feasible region of a linearized unconstrained binary polynomial optimization problem. We define an equivalent … Read more

    A dynamic approach to a proximal-Newton method for monotone inclusions in Hilbert spaces, with complexity $\bigo(1/n^2)$

  • M. Marques Alves
  • Hédy Attouch
  • Benar Fux Svaiter
    • Categories Convex and Nonsmooth Optimization

    In a Hilbert setting, we introduce a new dynamic system and associated algorithms aimed at solving by rapid methods, monotone inclusions. Given a maximal monotone operator $A$, the evolution is governed by the time dependent operator $I -(I + \lambda(t) {A})^{-1}$, where, in the resolvent, the positive control parameter $\lambda(t)$ tends to infinity as $t … Read more

    A cone-continuity constraint qualification and algorithmic consequences

  • Roberto Andreani
  • José Mario Martínez
  • Alberto Ramos
  • Paulo J. S. Silva
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    Every local minimizer of a smooth constrained optimization problem satisfies the sequential Approximate Karush-Kuhn-Tucker (AKKT) condition. This optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms. It is natural to ask for conditions on the constraints under which AKKT implies KKT. These conditions will be called Strict Constraint Qualifications … Read more

    A mixed integer programming approach to reduce fuel load accumulation for prescribed burn planning

  • John W Hearne
  • Melih Ozlen
  • Ramya Rachmawati
  • Karin Reinke
    • Categories Applications - OR and Management Sciences Tags , , , , ,

    The increasing frequency of destructive wild land fires, with a consequent loss of life and property, has led to fire and land management agencies initiating extensive fuel management programs. This involves long-term scheduling of the location of fuel reduction activities such as prescribed burning or mechanical clearing. In this paper a Mixed Integer Programming (MIP) … Read more

    The Cyclic Block Conditional Gradient Method for Convex Optimization Problems

  • Amir Beck
  • Shoham Sabach
  • Edouard Pauwels
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization Tags , , , , ,

    In this paper we study the convex problem of optimizing the sum of a smooth function and a compactly supported non-smooth term with a specific separable form. We analyze the block version of the generalized conditional gradient method when the blocks are chosen in a cyclic order. A global sublinear rate of convergence is established … Read more

    Alternating direction methods for non convex optimization with applications to second-order least-squares and risk parity portfolio selection

  • Xi Bai
  • Katya Scheinberg
    • Categories Finance and Economics, Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , , ,

    In this paper we mainly focus on optimization of sums of squares of quadratic functions, which we refer to as second-order least-squares problems, subject to convex constraints. Our motivation arises from applications in risk parity portfolio selection. We generalize the setting further by considering a class of nonlinear, non convex functions which admit a (non … Read more

    A corrected semi-proximal ADMM for multi-block convex optimization and its application to DNN-SDPs

  • Shaohua Pan
  • Li Shen
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    In this paper we propose a corrected semi-proximal ADMM (alternating direction method of multipliers) for the general $p$-block $(p\!\ge 3)$ convex optimization problems with linear constraints, aiming to resolve the dilemma that almost all the existing modified versions of the directly extended ADMM, although with convergent guarantee, often perform substantially worse than the directly extended … Read more