Optimization of Stochastic Problems with Probability Functions via Differential Evolution

  • Bayrammyrat Myradov
    • Categories Basic Sciences Applications, Stochastic Approaches, Stochastic Programming

    Chance constrained programming, quantile/Value-at-Risk (VaR) optimization and integral quantile / Conditional Value-at-Risk (CVaR) optimization problems as Stochastic Programming Problems with Probability Functions (SPP-PF) are one of the most widely studied optimization problems in recent years. As a rule real-life SPP-PF is nonsmooth nonconvex optimization problem with complex geometry of objective function. Moreover, often it cannot … Read more

    Convergent Prediction-Correction-based ADMM for multi-block separable convex programming

  • Zhao Pengjun
  • Chang Xiaokai
  • Liu Sanyang
  • Li Xu
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization Tags , , , , ,

    The direct extension of the classic alternating direction method with multipliers (ADMMe) to the multi-block separable convex optimization problem is not necessarily convergent, though it often performs very well in practice. In order to preserve the numerical advantages of ADMMe and obtain convergence, many modified ADMM were proposed by correcting the output of ADMMe or … Read more

    Global Optimisation of Multi-Plant Manganese Alloy Production

  • Henrik Andersson
  • Stein Wasbø
  • Martin Digernes
  • Brage Rugstad Knudsen
  • Lars Rudi
  • Magnus Stålhane
    • Categories Global Optimization Applications, Production and Logistics, Supply Chain Management

    This paper studies the problem of multi-plant manganese alloy production. The problem consists of finding the optimal furnace feed of ores, fluxes, coke, and slag that yields output products which meet customer specifications, and to optimally decide the volume, composition, and allocation of the slag. To solve the problem, a nonlinear pooling problem formulation is … Read more

    Approximations to Stochastic Dynamic Programs via Information Relaxation Duality

  • Santiago Balseiro
  • David B. Brown
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming Tags , , , , , ,

    In the analysis of complex stochastic dynamic programs, we often seek strong theoretical guarantees on the suboptimality of heuristic policies. One technique for obtaining performance bounds is perfect information analysis: this approach provides bounds on the performance of an optimal policy by considering a decision maker who has access to the outcomes of all future … Read more

    On the Convergence Rate of the Halpern-Iteration

  • Felix Lieder
    • Categories Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , ,

    In this work, we give a tight estimate of the rate of convergence for the Halpern-Iteration for approximating a fixed point of a nonexpansive mapping in a Hilbert space. Specifically, we prove that the norm of the residuals is upper bounded by the distance of the initial iterate to the closest fixed point divided by … Read more

    Accelerating block coordinate descent methods with identification strategies

  • Ronaldo Lopes
  • Sandra Augusta Santos
  • Paulo J. S. Silva
    • Categories Bound-constrained Optimization

    This work is about active set identification strategies aimed at accelerating block-coordinate descent methods (BCDM) applied to large-scale problems. We start by devising an identification function tailored for bound-constrained composite minimization together with an associated version of the BCDM, called Active BCDM, that is also globally convergent. The identification function gives rise to an efficient … Read more

    Uniqueness of Market Equilibria on Networks with Transport Costs

  • Vanessa Krebs
  • Martin Schmidt
    • Categories Applications - OR and Management Sciences, Convex and Nonsmooth Optimization, Network Optimization Tags , , , ,

    We study the existence and uniqueness of equilibria for perfectly competitive markets in capacitated transport networks. The model under consideration is rather general so that it captures basic aspects of related models in, e.g., gas or electricity networks. We formulate the market equilibrium model as a mixed complementarity problem and show the equivalence to a … Read more

    Unifying abstract inexact convergence theorems and block coordinate variable metric iPiano

  • Peter Ochs
    • Categories Nonsmooth Optimization Tags , , , , , , , , ,

    An abstract convergence theorem for a class of generalized descent methods that explicitly models relative errors is proved. The convergence theorem generalizes and unifies several recent abstract convergence theorems. It is applicable to possibly non-smooth and non-convex lower semi-continuous functions that satisfy the Kurdyka–Lojasiewicz (KL) inequality, which comprises a huge class of problems. Most of … Read more

    Nonconvex Equilibrium Models for Gas Market Analysis: Failure of Standard Techniques and Alternative Modeling Approaches

  • Veronika Grimm
  • Julia Grübel
  • Lars Schewe
  • Martin Schmidt
  • Gregor Zöttl
    • Categories Applications - OR and Management Sciences, Finance and Economics, Nonlinear Optimization Tags , , , , ,

    This paper provides a first approach to assess gas market interaction on a network with nonconvex flow models. In the simplest possible setup that adequately reflects gas transport and market interaction, we elaborate on the relation of the solution of a simultaneous competitive gas market game, its corresponding mixed nonlinear complementarity problem (MNCP), and a … Read more

    A Branch-and-Price Algorithm for Capacitated Hypergraph Vertex Separation

  • Michael Bastubbe
  • Marco E. Lübbecke
    • Categories 0-1 Programming, Combinatorial Optimization

    We exactly solve the NP-hard combinatorial optimization problem of finding a minimum cardinality vertex separator with k (or arbitrarily many) capacitated shores in a hypergraph. We present an exponential size integer programming formulation which we solve by branch-and-price. The pricing problem, an interesting optimization problem on its own, has a decomposable structure that we exploit … Read more