Infinite Dimensional Optimization

Optimality-Based Discretization Methods for the Global Optimization of Nonconvex Semi-Infinite Programs

  • Evren Turan
  • Johannes Jäschke
  • Rohit Kannan
    • Categories Global Optimization, Semi-infinite Programming Tags , , , , ,

    We use sensitivity analysis to design optimality-based discretization (cutting-plane) methods for the global optimization of nonconvex semi-infinite programs (SIPs). We begin by formulating the optimal discretization of SIPs as a max-min problem and propose variants that are more computationally tractable. We then use parametric sensitivity theory to design an efficient method for solving these max-min … Read more

    Semi-Infinite Mixed Binary and Disjunctive Programs: Applications to Set-Covering with Infinite Demand Points and Implicit Hitting Set Problems

  • Manish Bansal
    • Categories Combinatorial Optimization, Integer Programming, Semi-infinite Programming

    Sherali and Adams [Discrete Applied Math. 157: 1319-1333, 2009] derived convex hull of semi-infinite mixed binary linear programs (SIMBLPs) using Reformulation-Linearization Technique (RLT). In this paper, we study semi-infinite disjunctive programs (SIDPs — a generalization of SIMBLPs) and present linear programming equivalent and valid inequalities for them. We utilize these results for deriving a hierarchy … Read more

    Semi-Infinite Generalized Disjunctive and Mixed Integer Convex Programs with(out) Uncertainty

  • Manish Bansal
    • Categories 0-1 Programming, Convex Optimization, Semi-infinite Programming

    In this paper, we introduce semi-infinite generalized disjunctive programs that are defined by logical propositions along with disjunctions of sets of logical equations and infinite number of algebraic inequalities. We denote these programs by SIGDPs. For SIGDPs with linear and convex inequalities, we present new reformulations: semi-infinite mixed-binary/disjunctive linear programs and semi-infinite mixed-binary/disjunctive convex programs, … Read more

    Gas Transport Network Optimization: PDE-Constrained Models

  • Falk M. Hante
  • Martin Schmidt
    • Categories Applications - Science and Engineering, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    The optimal control of gas transport networks was and still is a very important topic for modern economies and societies. Accordingly, a lot of research has been carried out on this topic during the last years and decades. Besides mixed-integer aspects in gas transport network optimization, one of the main challenges is that a physically … Read more

    Duality in convex stochastic optimization

  • Teemu Pennanen
  • Ari-Pekka Perkkiö
    • Categories Convex Optimization, Infinite Dimensional Optimization, Stochastic Programming Tags , , ,

    This paper studies duality and optimality conditions in general convex stochastic optimization problems introduced by Rockafellar and Wets in \cite{rw76}. We derive an explicit dual problem in terms of two dual variables, one of which is the shadow price of information while the other one gives the marginal cost of a perturbation much like in … Read more

    Semi-infinite models for equilibrium selection

  • Maren Beck
  • Oliver Stein
    • Categories Game Theory, Multi-Criteria Optimization, Semi-infinite Programming Tags , , , ,

    In their seminal work `A General Theory of Equilibrium Selection in Games’ (The MIT Press, 1988) Harsanyi and Selten introduce the notion of payoff dominance to explain how players select some solution of a Nash equilibrium problem from a set of nonunique equilibria. We formulate this concept for generalized Nash equilibrium problems, relax payoff dominance … Read more

    Optimal Robust Policy for Feature-Based Newsvendor

  • Luhao Zhang
  • Jincheng Yang
  • Rui Gao
    • Categories Infinite Dimensional Optimization, Robust Optimization, Supply Chain Management Tags , , ,

    We study policy optimization for the feature-based newsvendor, which seeks an end-to-end policy that renders an explicit mapping from features to ordering decisions. Unlike existing works that restrict the policies to some parametric class which may suffer from sub-optimality (such as affine class) or lack of interpretability (such as neural networks), we aim to optimize … Read more

    A Stochastic Bregman Primal-Dual Splitting Algorithm for Composite Optimization

  • Antonio Silveti-Falls
  • Cesare Molinari
  • Jalal Fadili
    • Categories Convex and Nonsmooth Optimization, Infinite Dimensional Optimization, Stochastic Programming Tags , , , , , , , ,

    We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoothness assumptions, in which we allow for stochastic error in the computation of gradient terms within the algorithm. We show ergodic convergence in expectation of the Lagrangian optimality gap with a … Read more

    On approximate solutions for robust semi-infinite multi-objective convex symmetric cone optimization

  • Baha Alzalg
  • Amira Achouak Oulha
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Semi-infinite Programming Tags , , , ,

    We present approximate solutions for the robust semi-infinite multi-objective convex symmetric cone programming problem. By using the robust optimization approach, we establish an approximate optimality theorem and approximate duality theorems for approximate solutions in convex symmetric cone optimization problem involving infinitely many constraints to be satisfied and multiple objectives to be optimized simultaneously under the … Read more

    Sinkhorn Distributionally Robust Optimization

  • Jie Wang
  • Rui Gao
  • Yao Xie
    • Categories Infinite Dimensional Optimization, Robust Optimization, Stochastic Programming

    We study distributionally robust optimization (DRO) with Sinkhorn distance—a variant of Wasserstein distance based on entropic regularization. We derive convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. Compared with Wasserstein DRO, our proposed approach offers enhanced computational tractability for a broader class of loss functions, and the worst-case distribution exhibits … Read more