On complexity constants of linear and quadratic models for derivative-free trust-region algorithms

  • A. E. Schwertner
  • Francisco N. C. Sobral
    • Categories Nonlinear Optimization Tags , , ,

    Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing complexity results hide the dimensions of the problem. This work organizes several results in literature about bounds that appear in derivative-free trust-region algorithms based on linear … Read more

    A Constraint Dissolving Approach for Nonsmooth Optimization over the Stiefel Manifold

  • Xiaoyin Hu
  • Nachuan Xiao
  • Xin Liu
  • Kim-Chuan Toh
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    This paper focus on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-friendly objective functions. We propose a constraint dissolving function named NCDF and show that it has the same first-order stationary points and local minimizers as the original problem in … Read more

    A Ramsey-Type Equilibrium Model with Spatially Dispersed Agents

  • Leonhard Frerick
  • Georg Müller-Fürstenberger
  • Martin Schmidt
  • Max Späth
    • Categories Complementarity and Variational Inequalities, Finance and Economics Tags , , ,

    We present a spatial and time-continuous Ramsey-type equilibrium model for households and firms that interact on a spatial domain to model labor mobility in the presence of commuting costs. After discretization in space and time, we obtain a mixed complementarity problem that represents the spatial equilibrium model. We prove existence of equilibria using the theory … Read more

    Conditional Distributionally Robust Functionals

  • Alexander Shapiro
  • Alois Pichler
    • Categories Stochastic Programming Tags , , , ,

    Risk measures incorporate a conservative or risk averse perspective in decisionmaking under uncertainty. Taking a variety of models for the potential outcomes into account, the distributionally robust decision is the most conservative decision among the decisions available. This paper investigates different versions of conditional risk measures and distributionally robust functionals in a multistage setting. The … Read more

    Logic-based Benders decomposition with a partial assignment acceleration technique for avionics scheduling

  • Emil Karlsson
  • Elina Rönnberg
    • Categories (Mixed) Integer Linear Programming Tags , , , , ,

    Pre-runtime scheduling of large-scale electronic systems, as those in modern aircraft, can be computationally challenging. In this paper, we study a distributed integrated modular avionic system of practical relevance where the scheduling includes to assign communication messages to time slots and to sequence tasks on modules. For this problem, the challenge is the huge number … Read more

    A Proximal Gradient Method for Multi-objective Optimization Problems Using Bregman Functions

  • Md Abu Talhamainuddin Ansary
  • Joydeep Dutta
    • Categories Convex Optimization, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper, a globally convergent proximal gradient method is developed for convex multi-objective optimization problems using Bregman distance. The proposed method is free from any kind of a priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a subproblem is solved to find a descent direction. This … Read more

    Partitioning through projections: strong SDP bounds for large graph partition problems

  • Frank de Meijer
  • Renata Sotirov
  • Angelika Wiegele
  • Shudian Zhao
    • Categories Semi-definite Programming Tags , , , ,

    The graph partition problem (GPP) aims at clustering the vertex set of a graph into a fixed number of disjoint subsets of given sizes such that the sum of weights of edges joining different sets is minimized. This paper investigates the quality of doubly nonnegative (DNN) relaxations, i.e., relaxations having matrix variables that are both … Read more

    A new family of route formulations for split delivery vehicle routing problems

  • Isaac Balster
  • Teobaldo Bulhões
  • Pedro Munari
  • Artur Alves Pessoa
  • Ruslan Sadykov
    • Categories Combinatorial Optimization, Integer Programming, Transportation Tags , , , ,

    We propose a new family of formulations with route-based variables for the split delivery vehicle routing problem with and without time windows. Each formulation in this family is characterized by the maximum number of different demand quantities that can be delivered to a customer during a vehicle visit. As opposed to previous formulations in the … Read more

    Optimal Reconfiguration with Variant Transmission Times on Network

  • Shiva Prakash Gupta
  • Urmila Pyakurel
  • Tanka Nath Dhamala
    • Categories Applications - OR and Management Sciences, Network Optimization, Transportation Tags , , , ,

    Contraflow means lane reversals on networks. In lane reversal reconfiguration, the capacity of arc increases by reorienting arcs towards demand nodes, which maximizes the flow value and reduces the travel time. In this work, we survey the existing pieces of literature on single and multi-commodity contraflow problems with symmetric and asymmetric travel times on parallel … Read more

    Monotonicity and Complexity of Multistage Stochastic Variational Inequalities

  • Jie Jiang
  • Hailin Sun
    • Categories Complementarity and Variational Inequalities, Stochastic Programming Tags , , ,

    In this paper, we consider multistage stochastic variational inequalities (MSVIs). First, we give multistage stochastic programs and multistage multi-player noncooperative game problems as source problems. After that, we derive the monotonicity properties of MSVIs under less restrictive conditions. Finally, the polynomial rate of convergence with respect to sample sizes between the original problem and its … Read more