Stationarity and regularity of infinite collections of sets. Applications to infinitely constrained optimization

  • Alexander Y. Kruger
  • Marco A. López
    • Categories Nonsmooth Optimization, Semi-infinite Programming Tags , , , , , , , ,

    This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger & L�pez (2012) and is mainly focused on the application of the criteria from Kruger & L�pez (2012) to infinitely constrained optimization problems. We consider several settings of optimization problems which involve (explicitly … Read more

    Proximal Methods with Bregman Distances to Solve VIP on Hadamard manifolds

  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
    • Categories Global Optimization, Global Optimization Theory Tags , , , ,

    We present an extension of the proximal point method with Bregman distances to solve Variational Inequality Problems (VIP) on Hadamard manifolds (simply connected finite dimensional Riemannian manifold with nonpositive sectional curvature). Under some natural assumption, as for example, the existence of solutions of the (VIP) and the monotonicity of the multivalued vector field, we prove … Read more

    Modifications of the limited-memory BNS method for better satisfaction of previous quasi-Newton conditions

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , , ,

    Several modifications of the limited-memory variable metric BNS method for large scale unconstrained optimization are proposed, which consist in corrections (derived from the idea of conjugate directions) of the used di®erence vectors to improve satisfaction of previous quasi-Newton conditions, utilizing information from previous or subsequent iterations. In case of quadratic objective functions, conjugacy of all … Read more

    A lifting method for generalized semi-infinite programs based on lower level Wolfe duality

  • Moritz Diehl
  • Oliver Stein
  • Boris Houska
  • Paul Steuermann
    • Categories Complementarity and Variational Inequalities, Robust Optimization, Semi-infinite Programming Tags , , , ,

    This paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be … Read more

    A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms

  • Laurent Condat
    • Categories Convex and Nonsmooth Optimization Tags , , , , , , , , ,

    We propose a new first-order splitting algorithm for solving jointly the primal and dual formulations of large-scale convex minimization problems involving the sum of a smooth function with Lipschitzian gradient, a nonsmooth proximable function, and linear composite functions. This is a full splitting approach in the sense that the gradient and the linear operators involved … Read more

    Continuous convex sets and zero duality gap for convex programs

  • Emil Ernst
  • Michel Volle
    • Categories Convex Optimization Tags , , , ,

    This article uses classical notions of convex analysis over euclidean spaces, like Gale & Klee’s boundary rays and asymptotes of a convex set, or the inner aperture directions defined by Larman and Brøndsted for the same class of sets, to provide a new zero duality gap criterion for ordinary convex programs. On this ground, we … Read more

    Zero duality gap for convex programs: a general result

  • Emil Ernst
  • Michel Volle
    • Categories Convex Optimization Tags , ,

    This article addresses a general criterion providing a zero duality gap for convex programs in the setting of the real locally convex spaces. The main theorem of our work is formulated only in terms of the constraints of the program, hence it holds true for any objective function fulfilling a very general qualification condition, implied … Read more

    Closed means continuous iff polyhedral: a converse of the GKR theorem

  • Emil Ernst
    • Categories Convex Optimization Tags , , , , ,

    Given x, a point of a convex subset C of an Euclidean space, the two following statements are proven to be equivalent: (i) any convex function f : C → R is upper semi-continuous at x, and (ii) C is polyhedral at x. In the particular setting of closed convex mappings and Fσ domains, we … Read more

    Models for managing the impact of an epidemic

  • Daniel Bienstock
  • A. Cecilia Zenteno
    • Categories Applications - OR and Management Sciences, Biomedical Applications Tags ,

    In this paper we consider robust models of surge capacity plans to be deployed in the event of a flu pandemic. In particular, we focus on managing critical staff levels at organizations that must remain operational during such an event. We develop efficient procedures for managing emergency resources so as to minimize the impact of … Read more

    Strong formulations for convex functions over nonconvex sets

  • Daniel Bienstock
  • Alexander Michalka
    • Categories Global Optimization, Nonsmooth Optimization, Second-Order Cone Programming Tags , ,

    In this paper we derive strong linear inequalities for sets of the form {(x, q) ∈ R^d × R : q ≥ Q(x), x ∈ R^d − int(P ) }, where Q(x) : R^d → R is a quadratic function, P ⊂ R^d and “int” denotes interior. Of particular but not exclusive interest is the … Read more