Efficient search strategies for constrained multiobjective blackbox optimization

  • Sébastien Le Digabel
  • anles
  • Ludovic Salomon
  • Christophe Tribes
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags ,

    Multiobjective blackbox optimization deals with problems where the objective and constraint functions are the outputs of a numerical simulation. In this context, no derivatives are available, nor can they be approximated by finite differences, which precludes the use of classical gradient-based techniques. The DMulti-MADS algorithm implements a state-of-the-art direct search procedure for multiobjective blackbox optimization … Read more

    New Algorithms for maximizing the difference of convex functions

  • Aharon Ben-Tal
  • Luba Tetruashvili
    • Categories Global Optimization, Global Optimization Applications, Nonlinear Optimization

    Maximizing the difference of 2 convex functions over a convex feasible set (the so called DCA problem) is a hard problem. There is a large number of publications addressing this problem. Many of them are variations of widely used DCA algorithm [20]. The success of this algorithm to reach a good approximation of a global … Read more

    Cost allocation in maintenance clustering

  • Andries van Beek
  • Loe Schlicher
    • Categories Applications - OR and Management Sciences, Game Theory Tags , , , ,

    Inspired by collaborative initiatives in the military domain, we analyze a setting in which multiple different players (e.g., Ministries of Defence) have to carry out preventive maintenance jobs. Each player is responsible for one job, with a job-specific minimal frequency and with maintenance costs, consisting of a job-specific variable component and a fixed component, which … Read more

    Optimistic Noise-Aware Sequential Quadratic Programming for Equality Constrained Optimization with Rank-Deficient Jacobians

  • Jiahao Shi
  • Baoyu Zhou
  • Albert S. Berahas
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

    We propose and analyze a sequential quadratic programming algorithm for minimizing a noisy nonlinear smooth function subject to noisy nonlinear smooth equality constraints. The algorithm uses a step decomposition strategy and, as a result, is robust to potential rank-deficiency in the constraints, allows for two different step size strategies, and has an early stopping mechanism. … Read more

    Facial approach for constructing stationary points for mathematical programs with cone complementarity constraints

  • Javier I. Madariaga
  • Héctor Ramírez
    • Categories Complementarity and Variational Inequalities, Cone Programming Tags , , ,

    This paper studies stationary points in mathematical programs with cone complementarity constraints (CMPCC). We begin by reviewing various formulations of CMPCC and revisiting definitions for Bouligand, proximal strong, regular strong, Wachsmuth’s strong, L-strong, weak, as well as Mordukhovich and Clarke stationary points, establishing a comprehensive framework for CMPCC. Building on key principles related to cone … Read more

    A note on asynchronous Projective Splitting in Julia

  • Utkarsh Sharma
  • Kashish Goel
  • Aryan Dua
  • Sebastian Pokutta
  • Zev Woodstock
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization, Parallel Algorithms

    While it has been mathematically proven that Projective Splitting (PS) algorithms can converge in parallel and distributed computing settings, to-date, it appears there were no open-source implementations of the full algorithm with asynchronous computing capabilities. This note fills this gap by providing a Julia implementation of the asynchronous PS algorithm of Eckstein and Combettes for … Read more

    Solving unbounded optimal control problems with the moment-SOS hierarchy

  • Karolina Sehnalova
  • Didier Henrion
  • Milan Korda
  • Martin Kružík
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , , ,

    The behaviour of the moment-sums-of-squares (moment-SOS) hierarchy for polynomial optimal control problems on compact sets has been explored to a large extent. Our contribution focuses on the case of non-compact control sets. We describe a new approach to optimal control problems with unbounded controls, using compactification by partial homogenization, leading to an equivalent infinite dimensional … Read more

    Strategic design of collection and delivery point networks for urban parcel distribution

  • Benjamin Rojas
  • Homero Larrain
  • Mathias A. Klapp
    • Categories Applications - OR and Management Sciences, Production and Logistics, Transportation Tags , , ,

    Collection and delivery points (CDPs) allow logistics operators to consolidate multiple customer request deliveries on a single vehicle stop, reducing distribution costs. However, for customers to adopt CDPs, they must be willing to travel to a nearby CDP to pick up their parcels. This choice depends on personal preferences, the proximity of CDPs, and economic … Read more

    An extrapolated and provably convergent algorithm for nonlinear matrix decomposition with the ReLU function

  • Nicolas Gillis
  • Margherita Porcelli
  • Giovanni Seraghiti
    • Categories Data Science Algorithms, Optimization in Data Science, Other Topics Tags , ,

    Nonlinear matrix decomposition (NMD) with the ReLU function, denoted ReLU-NMD, is the following problem: given a sparse, nonnegative matrix \(X\) and a factorization rank \(r\), identify a rank-\(r\) matrix \(\Theta\) such that \(X\approx \max(0,\Theta)\). This decomposition finds application in data compression, matrix completion with entries missing not at random, and manifold learning. The standard ReLU-NMD … Read more