A new sufficient condition for non-convex sparse recovery via weighted $\ell_r\!-\!\ell_1$ minimization

  • Jianwen Huang
  • Feng Zhang
    • Categories Data-Mining, Nonsmooth Optimization Tags , , ,

    In this letter, we discuss the reconstruction of sparse signals from undersampled data, which belongs to the core content of compressed sensing. A new sufficient condition in terms of the restricted isometry constant (RIC) and restricted orthogonality constant (ROC) is first established for the performance guarantee of recently proposed non-convex weighted $\ell_r-\ell_1$ minimization in recovering … Read more

    CliSAT: a SAT-based exact algorithm for hard maximum clique problems

  • Pablo San Segundo
  • Fabio Furini
  • David Alvarez
  • Panos M. Pardalos
    • Categories Combinatorial Optimization, Game Theory Tags , , ,

    Given a graph, the maximum clique problem (MCP) asks for determining a complete subgraph with the largest possible number of vertices. We propose a new exact algorithm, called CliSAT, to solve the MCP to proven optimality. This problem is of fundamental importance in graph theory and combinatorial optimization due to its practical relevance for a … Read more

    A decomposition method for lasso problems with zero-sum constraint

  • Andrea Cristofari
    • Categories Nonlinear Optimization Tags , , , ,

    In this paper, we consider lasso problems with zero-sum constraint, commonly required for the analysis of compositional data in high-dimensional spaces. A novel algorithm is proposed to solve these problems, combining a tailored active-set technique, to identify the zero variables in the optimal solution, with a 2-coordinate descent scheme. At every iteration, the algorithm chooses … Read more

    A level-set-based topology optimization strategy using radial basis functions and a Hilbertian velocity extension

  • Giovanna Castelloa Andrade
  • Sandra A. Santos
    • Categories Mechanical Engineering, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Tags , , , ,

    This work addresses the structural compliance minimization problem through a level-set-based strategy that rests upon radial basis functions with compact support combined with Hilbertian velocity extensions. A consistent augmented Lagrangian scheme is adopted to handle the volume constraint. The linear elasticity model and the variational problem associated with the computation of the velocity field are … Read more

    Advancements in the computation of enclosures for multi-objective optimization problems

  • Gabriele Eichfelder
  • Leo Warnow
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. One solution to overcome this problem is to compute an enclosure, a special kind of coverage, of the nondominated set. One … Read more

    Distributionally Robust Disaster Relief Planning under the Wasserstein Set

  • Mohamed El Tonbari
  • George L. Nemhauser
  • Alejandro Toriello
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , ,

    We study a two-stage natural disaster management problem modeled as a stochastic program, where the first stage consists of a facility location problem, deciding where to open facilities and pre-allocate resources such as medical and food kits, and the second stage is a fixed-charge transportation problem, routing resources to affected areas after observing a disaster. … Read more

    Accelerating Stochastic Sequential Quadratic Programming for Equality Constrained Optimization using Predictive Variance Reduction

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

    In this paper, we propose a stochastic variance reduction method for solving equality constrained optimization problems. Specifically, we develop a method based on the sequential quadratic programming paradigm that utilizes gradient approximations via predictive variance reduction techniques. Under reasonable assumptions, we prove that a measure of first-order stationarity evaluated at the iterates generated by our … Read more

    Dynamic programming in convex stochastic optimization

  • Teemu Pennanen
  • Ari-Pekka Perkkiö
    • Categories Stochastic Programming Tags , ,

    This paper studies the dynamic programming principle for general convex stochastic optimization problems introduced by Rockafellar and Wets in the 1970s. We extend the applicability of the theory by relaxing compactness and boundedness assumptions. In the context of financial mathematics, the relaxed assumptions are satisfied under the well-known no-arbitrage condition and the reasonable asymptotic elasticity … Read more

    Courier satisfaction in rapid delivery systems using dynamic operating regions

  • Ramon Auad
  • Alan L. Erera
  • Martin Savelsbergh
    • Categories Applications - OR and Management Sciences, Production and Logistics, Transportation Tags , , , , ,

    Rapid delivery systems where an order is delivered to a customer from a local distribution point within minutes or hours have experienced rapid growth recently and often rely on gig economy couriers. The prime example is a meal delivery system. During an operating day, couriers in such a system are used to deliver orders placed … Read more

    An Adaptive Riemannian Gradient Method Without Function Evaluations

  • Geovani Nunes Grapiglia
  • Gabriel Stella
    • Categories Nonlinear Optimization Tags , ,

    In this paper we propose an adaptive gradient method for optimization on Riemannian manifolds. The update rule for the stepsizes relies only on gradient evaluations. Assuming that the objective function is bounded from below and that its gradient field is Lipschitz continuous, we establish worst-case complexity bounds for the number of gradient evaluations that the … Read more