Month: July 2018

Strictly and Γ-Robust Counterparts of Electricity Market Models: Perfect Competition and Nash-Cournot Equilibria

  • Anja Kramer
  • Vanessa Krebs
  • Martin Schmidt
    • Categories Finance and Economics, Game Theory, Robust Optimization Tags , , , ,

    This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the Γ-approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable … Read more

    Why is maximum clique often easy in practice?

  • Austin Buchanan
  • Jose L. Walteros
    • Categories Combinatorial Optimization

    To this day, the maximum clique problem remains a computationally challenging problem. Indeed, despite researchers’ best efforts, there exist unsolved benchmark instances with one thousand vertices. However, relatively simple algorithms solve real-life instances with millions of vertices in a few seconds. Why is this the case? Why is the problem apparently so easy in many … Read more

    The sharpest column: stabilizing column generation for the bin packing problem via a lexicographic pricer

  • Stefano Coniglio
  • Fabio D'Andreagiovanni
  • Fabio Furini
    • Categories Combinatorial Optimization, Integer Programming

    In spite of being an extremely successful method to tackle mathematical programs involving a very large number of variables, Column Generation (CG) is known to suffer from stabilization issues which can slow down its convergence significantly. In this article, we propose a new parameter-free stabilization technique for CG based on solving a lexicographic pricing problem. … Read more

    Efficient Solution of Maximum-Entropy Sampling Problems

  • Kurt M. Anstreicher
    • Categories (Mixed) Integer Nonlinear Programming, Convex Optimization, Statistics Tags , ,

    We consider a new approach for the maximum-entropy sampling problem (MESP) that is based on bounds obtained by maximizing a function of the form ldet M(x) over linear constraints, where M(x)is linear in the n-vector x. These bounds can be computed very efficiently and are superior to all previously known bounds for MESP on most … Read more

    Multistage Stochastic Demand-side Management for Price-Making Major Consumers of Electricity in a Co-optimized Energy and Reserve Market

  • Anthony Downward
  • Mahbubeh Habibian
  • Golbon Zakeri
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Energy Tags , ,

    In this paper we take an optimization-driven heuristic approach, motivated by dynamic programming, to solve a multistage stochastic optimization of energy consumption for a large manufacturer who is a price-making major consumer of electricity. We introduce a mixed-integer program that co-optimizes consumption bids and interruptible load reserve offers, for such a major consumer over a … Read more

    Decentralized Algorithms for Distributed Integer Programming Problems with a Coupling Cardinality Constraint

  • Shabbir Ahmed
  • George L. Nemhauser
  • Ezgi Karabulut
    • Categories 0-1 Programming, Parallel Algorithms Tags , ,

    We consider a multi-player optimization where each player has her own optimization problem and the individual problems are connected by a cardinality constraint on their shared resources. We give distributed algorithms that allow each player to solve their own optimization problem and still achieve a global optimization solution for problems that possess a concavity property. … Read more

    Dynamic Scheduling of Home Health Care Patients to Medical Providers

  • Andre Augusto Cire
  • Adam Diamant
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    Home care provides personalized medical care and social support to patients within their own home. Our work proposes a dynamic scheduling framework to assist in the assignment of patients to health practitioners (HPs) at a single home care agency. We model the decision of which patients to assign to HPs as a discrete-time Markov decision … Read more

    Finite convergence and weak sharpness for solutions of nonsmooth variational inequalities in Hilbert spaces

  • Qamrul Hasan Ansari
  • Luong Nguyen
  • Xiaolong Qin
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , ,

    This paper deals with the study of weak sharp solutions for nonsmooth variational inequalities and finite convergence property of the proximal point method. We present several characterizations for weak sharpness of the solutions set of nonsmooth variational inequalities without using the gap functions. We show that under weak sharpness of the solutions set, the sequence … Read more

    Coordination of a two-level supply chain with contracts

  • Safia Kedad-Sidhoum
  • Fanny Pascual
  • Siao-Leu Phouratsamay
    • Categories Dynamic Programming, Production and Logistics, Supply Chain Management Tags , , , ,

    We consider the coordination of planning decisions of a single product in a supply chain composed of one supplier and one retailer, by using contracts. We assume that the retailer has the market power: he can impose his optimal replenishment plan to the supplier. Our aim is to minimize the supplier’s cost without increasing the … Read more

    A stochastic Levenberg-Marquardt method using random models with complexity results and application to data assimilation

  • Elhoucine Bergou
  • Youssef Diouane
  • Vyacheslav Kungurtsev
  • Clément W. Royer
    • Categories Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , , , ,

    Globally convergent variants of the Gauss-Newton algorithm are often the methods of choice to tackle nonlinear least-squares problems. Among such frameworks, Levenberg-Marquardt and trust-region methods are two well-established, similar paradigms. Both schemes have been studied when the Gauss-Newton model is replaced by a random model that is only accurate with a given probability. Trust-region schemes … Read more