A Derivative-Free Algorithm for Constrained Global Optimization based on Exact Penalty Functions

  • G. Di Pillo
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Global Optimization, Nonlinear Optimization

    Constrained global optimization problems can be tackled by using exact penalty approaches. In a preceding paper, we proposed an exact penalty algorithm for constrained problems which combines an unconstrained global minimization technique for minimizing a non-differentiable exact penalty func- tion for given values of the penalty parameter, and an automatic updating of the penalty parameter … Read more

    Derivative-free Robust Optimization for Circuit Design

  • A. Ciccazzo
  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
  • V. Latorre
    • Categories Nonlinear Optimization, Robust Optimization Tags

    In this paper, we introduce a framework for derivative-free robust optimization based on the use of an efficient derivative-free optimization routine for mixed integer nonlinear problems. The proposed framework is employed to find a robust optimal design of a particular integrated circuit (namely a DC-DC converter commonly used in portable electronic devices). The proposed robust … Read more

    Differentiability properties of metric projections onto convex sets

  • Alexander Shapiro
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    It is known that directional differentiability of metric projection onto a closed convex set in a finite dimensional space is not guaranteed. In this paper we discuss sufficient conditions ensuring directional differentiability of such metric projections. The approach is based on a general theory of sensitivity analysis of parameterized optimization problems. ArticleDownload View PDF

    Modeling with Metaconstraints and Semantic Typing of Variables

  • Andre Augusto Cire
  • John Hooker
  • Tallys H. Yunes
    • Categories Modeling Languages and Systems, Optimization Software Design Principles Tags , , ,

    Recent research in hybrid optimization shows that a combination of technologies that exploits their complementary strengths can significantly speed up computation. The use of high-level metaconstraints in the problem formulation can achieve a substantial share of these computational gains by better communicating problem structure to the solver. During the solution process, however, metaconstraints give rise … Read more

    A Parallel Quadratic Programming Method for Dynamic Optimization Problems

  • Moritz Diehl
  • Sebastian Sager
  • Janick V Frasch
    • Categories Control Applications, Quadratic Programming Tags , , ,

    Quadratic programming problems (QPs) that arise from dynamic optimization problems typically exhibit a very particular structure. We address the ubiquitous case where these QPs are strictly convex and propose a dual Newton strategy that exploits the block-bandedness similarly to an interior-point method. Still, the proposed method features warmstarting capabilities of active-set methods. We give details … Read more

    Variational analysis in psychological modeling

  • Boris S. Mordukhovich
  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , , , ,

    This paper develops some mathematical models arising in psychology and some other areas of behavioral sciences that are formalized via general preferences with variable ordering structures. Our considerations are based on the recent “variational rationality approach” that unifies numerous theories in different branches of behavioral sciences by using, in particular, worthwhile change and stay dynamics … Read more

    An inexact proximal path-following algorithm for constrained convex minimization

  • Volkan Cevher
  • Quoc Tran-Dinh
  • Anastasios Kyrillidis
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    Many scientific and engineering applications feature large-scale non-smooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the non-smooth objective is equipped with a tractable proximity operator and that the convex constraints afford a self-concordant barrier. We provide a new joint treatment … Read more

    Efficient upper and lower bounds for global mixed-integer optimal control

  • Mathieu Claeys
  • Sebastian Sager
  • Frédéric Messine
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Applications, Optimization of Simulated Systems

    We present a control problem for an electrical vehicle. Its motor can be operated in two discrete modes, leading either to acceleration and energy consumption, or to a recharging of the battery. Mathematically, this leads to a mixed-integer optimal control problem (MIOCP) with a discrete feasible set for the controls taking into account the electrical … Read more

    Singularly Perturbed Markov Decision Processes: A Multiresolution Algorithm

  • Chin Pang Ho
  • Panos Parpas
    • Categories Dynamic Programming Tags , , ,

    Singular perturbation techniques allow the derivation of an aggregate model whose solution is asymptotically optimal for Markov Decision Processes with strong and weak interactions. We develop an algorithm that takes advantage of the asymptotic optimality of the aggregate model in order to compute the solution of the original model with theoretically better complexity than conventional … Read more

    Dynamic Cost Allocation for Economic Lot Sizing Games

  • Alejandro Toriello
  • Nelson A. Uhan
    • Categories Game Theory, Production and Logistics Tags , ,

    We consider a cooperative game defined by an economic lot sizing problem with concave ordering costs over a finite time horizon, in which each player faces demand for a single product in each period and coalitions can pool orders. We show how to compute a dynamic cost allocation in the strong sequential core of this … Read more