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Learning how to play Nash, potential games and alternating minimization method for structured nonconvex problems on Riemannian manifolds

  • J. X. da Cruz Neto
  • Paulo Roberto Oliveira
  • Antoine Soubeyran
  • Pedro A. Soares Jr.
    • Categories Applications - Science and Engineering, Game Theory, Nonsmooth Optimization

    In this paper we consider minimization problems with constraints. We show that if the set of constaints is a Riemannian manifold of non positive curvature and the objective function is lower semicontinuous and satisfi es the Kurdyka-Lojasiewicz property, then the alternating proximal algorithm in Euclidean space is naturally extended to solve that class of problems. We … Read more

    On Differentiability Properties of Player Convex Generalized Nash Equilibrium Problems

  • Nadja Harms
  • Oliver Stein
  • Christian Kanzow
    • Categories Constrained Nonlinear Optimization, Game Theory, Nonsmooth Optimization Tags , , , , ,

    This article studies differentiability properties for a reformulation of a player convex generalized Nash equilibrium problem as a constrained and possibly nonsmooth minimization problem. By using several results from parametric optimization we show that, apart from exceptional cases, all locally minimal points of the reformulation are differentiability points of the objective function. This justifies a … Read more

    A Dynamic Programming Heuristic for the Quadratic Knapsack Problem

  • Franklin Djeumou Fomeni
  • Adam N. Letchford
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Dynamic Programming Tags , ,

    It is well known that the standard (linear) knapsack problem can be solved exactly by dynamic programming in O(nc) time, where n is the number of items and c is the capacity of the knapsack. The quadratic knapsack problem, on the other hand, is NP-hard in the strong sense, which makes it unlikely that it … Read more

    Efficient Cardinality/Mean-Variance Portfolios

  • R. P. Brito
  • Luis Nunes Vicente
    • Categories Finance and Economics, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , , ,

    A number of variants of the classical Markowitz mean-variance optimization model for portfolio selection have been investigated to render it more realistic. Recently, it has been studied the imposition of a cardinality constraint, setting an upper bound on the number of active positions taken in the portfolio, in an attempt to improve its performance and … Read more

    A Fast Algorithm for Constructing Efficient Event-Related fMRI Designs

  • Ming-Hung Kao
  • Hans D Mittelmann
    • Categories Biomedical Applications, Global Optimization Applications, Multi-Criteria Optimization

    We propose a novel, ecient approach for obtaining high-quality experimental designs for event-related functional magnetic resonance imaging (ER-fMRI). Our approach combines a greedy hillclimbing algorithm and a cyclic permutation method. When searching for optimal ER-fMRI designs, the proposed approach focuses only on a promising restricted class of designs with equal frequency of occurrence across stimulus … Read more

    A PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS

  • Tran Van Hao
  • Nguyen Huu Thong
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Stochastic Approaches Tags , , ,

    This paper proposes a new probabilistic algorithm for solving multi-objective optimization problems – Probability-Driven Search Algorithm. The algorithm uses probabilities to control the process in search of Pareto optimal solutions. Especially, we use the absorbing Markov Chain to argue the convergence of the algorithm. We test this approach by implementing the algorithm on some benchmark … Read more

    Time consistency of dynamic risk measures

  • Alexander Shapiro
    • Categories Dynamic Programming, Stochastic Programming Tags , , , ,

    In this paper we discuss time consistency of risk averse multistage stochastic programming problems. We show, in a framework of finite scenario trees, that composition of law invariant coherent risk measures can be law invariant only for the expectation or max-risk measures. Citation Preprint Article Download View Time consistency of dynamic risk measures

    Risk neutral and risk averse Stochastic Dual Dynamic Programming method

  • Joari Paulo da Costa
  • Alexander Shapiro
  • Murilo Pereira Soares
  • Wajdi Tekaya
    • Categories Dynamic Programming, Scheduling, Stochastic Programming Tags , , , , , ,

    In this paper we discuss risk neutral and risk averse approaches to multistage (linear) stochastic programming problems based on the Stochastic Dual Dynamic Programming (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system. Citation Article Download View Risk neutral and risk … Read more

    Error bounds for vector-valued functions on metric spaces

  • Ewa M. Bednarczuk
  • Alexander Y. Kruger
    • Categories Multi-Criteria Optimization, Nonsmooth Optimization Tags , , ,

    In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivative-like objects — slopes — are introduced and a classification scheme of error bound criteria is presented. Citation Published in Vietnam … Read more

    Optimizing Trading Decisions for Hydro Storage Systems using Approximate Dual Dynamic Programming

  • Nils Löhndorf
  • David Wozabal
  • Stefan Minner
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming Tags , , ,

    We propose a new approach to optimize operations of hydro storage systems with multiple connected reservoirs which participate in wholesale electricity markets. Our formulation integrates short-term intraday with long-term interday decisions. The intraday problem considers bidding decisions as well as storage operation during the day and is formulated as a stochastic program. The interday problem … Read more