A new explicit iterative algorithm for solving split variational inclusion and fixed point problem for the infinite family of nonexpansive operators

  • Zhihui Xu
  • Cuijie Zhang
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    In this paper, we introduce a new explicit iterative algorithm for finding a solution of split variational inclusion problem over the common fixed points set of a infinite family of nonexpansive mappings in Hilbert spaces. To reach this goal, the iterative algorithms which combine Tian’s method with some fixed point technically proving methods are utilized … Read more

    Newton-like method with diagonal correction for distributed optimization

  • Dragana Bajović
  • Dušan Jakovetić
  • Nataša Krejić
  • Nataša Krklec Jerinkić
    • Categories Nonlinear Optimization Tags , , ,

    We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are attractive due to their inexpensive iterations, but have a drawback of slow convergence rates. This motivates the incorporation of second-order information … Read more

    Variational principles, completeness and the existence of traps in behavioral sciences

  • Stephan Cobzas
  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Applications - Science and Engineering, Nonlinear Optimization

    In this paper, driven by Behavioral applications to human dynamics, we consider the characterization of completeness in pseudo-quasimetric spaces in term of a generalization of Ekeland’s variational principle in such spaces, and provide examples illustrating significant improvements to some previously obtained results, even in complete metric spaces. At the behavioral level, we show that the … Read more

    A State Transition MIP Formulation for the Unit Commitment Problem

  • Semih Atakan
  • Guglielmo Lulli
  • Suvrajeet Sen
    • Categories Applications - OR and Management Sciences Tags ,

    In this paper, we present the state-transition formulation for the unit commitment problem. This formulation is based on the definition of new decision variables, which, instead of indicating the on/off statuses of a generator, captures its state transitions between consecutive time periods. We show that this new approach produces a formulation which naturally includes valid … Read more

    Remark on multi-target,robust linear-quadratic control problem on semi-infinite interval

  • Leonid Faybusovich
  • Thanasak Mouktonglang
    • Categories Control Applications, Infinite Dimensional Optimization Tags ,

    We consider multi-target,robust linear-quadratic control problem on semi-infinite interval. Using functional-analytic approach developed in [2], we reduce this problem to a convex optimization problem on the simplex. Explicit procedure for the reduced optimization problem is described. CitationPreprint, University of Notre Dame, August,2015ArticleDownload View PDF

    Integer Programming Approaches for Appointment Scheduling with Random No-shows and Service Durations

  • Ruiwei Jiang
  • Siqian Shen
  • Yiling Zhang
    • Categories (Mixed) Integer Linear Programming, Scheduling, Stochastic Programming

    We consider a single-server scheduling problem given a fixed sequence of appointment arrivals with random no-shows and service durations. The probability distribution of the uncertain parameters is assumed to be ambiguous and only the support and first moments are known. We formulate a class of distributionally robust (DR) optimization models that incorporate the worst-case expectation/conditional … Read more

    A new family of facet defining inequalities for the maximum edge-weighted clique problem

  • Franklin Djeumou Fomeni
    • Categories 0-1 Programming, Combinatorial Optimization, Cutting Plane Approaches Tags , , , , ,

    This paper considers a family of cutting planes, recently developed for mixed 0-1 polynomial programs and shows that they define facets for the maximum edge-weighted clique problem. There exists a polynomial time exact separation algorithm for these in- equalities. The result of this paper may contribute to the development of more efficient algorithms for the … Read more

    Borwein–Preiss Vector Variational Principle

  • Alexander Y. Kruger
  • Somyot Plubtieng
  • Thidaporn Seangwattana
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    This article extends to the vector setting the results of our previous work Kruger et al. (2015) which refined and slightly strengthened the metric space version of the Borwein–Preiss variational principle due to Li and Shi, J. Math. Anal. Appl. 246(1), 308–319 (2000). We introduce and characterize two seemingly new natural concepts of epsilon-minimality, one … Read more

    Generalized Uniformly Optimal Methods for Nonlinear Programming

  • Saeed Ghadimi
  • Guanghui Lan
  • Hongchao Zhang
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , , ,

    In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search step (gradient descent or Quasi-Newton iteration) into these uniformly optimal convex programming methods, and then enforce a monotone decreasing property of … Read more

    On Theoretical and Numerical Aspects of the Shape Sensitivity Analysis for the 3D Time-dependent Maxwell’s Equations

  • Stephan Schmidt
  • Maria Schütte
  • Andrea Walther
    • Categories Optimization of Systems modeled by PDEs Tags , , , , ,

    We propose a novel approach using shape derivatives to solve inverse optimization problems governed by Maxwell’s equations, focusing on identifying hidden geometric objects in a predefined domain. The target functional is of tracking type and determines the distance between the solution of a 3D time-dependent Maxwell problem and given measured data in an $L_2$-norm. Minimization … Read more