Dice-sion Making under Uncertainty: When Can a Random Decision Reduce Risk?

  • Erick Delage
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Robust Optimization, Stochastic Programming

    Stochastic programming and distributionally robust optimization seek deterministic decisions that optimize a risk measure, possibly in view of the most adverse distribution in an ambiguity set. We investigate under which circumstances such deterministic decisions are strictly outperformed by random decisions which depend on a randomization device producing uniformly distributed samples that are independent of all … Read more

    Data-Driven Risk-Averse Stochastic Program And Renewable Energy Integration

  • Chaoyue Zhao
    • Categories Applications - OR and Management Sciences Tags , ,

    With increasing penetration of renewable energy into the power grid and its intermittent nature, it is crucial and challenging for system operators to provide reliable and cost effective daily electricity generation scheduling. In this dissertation, we present our recently developed innovative modeling and solution approaches to address this challenging problem. We start with developing several … Read more

    A simple preprocessing algorithm for semidefinite programming

  • Preston Faulk
  • Gabor Pataki
  • Quoc Tran-Dinh
    • Categories Convex Optimization, Optimization Software Benchmark, Semi-definite Programming

    We propose a very simple preprocessing algorithm for semidefinite programming. Our algorithm inspects the constraints of the problem, deletes redundant rows and columns in the constraints, and reduces the size of the variable matrix. It often detects infeasibility. Our algorithm does not rely on any optimization solver: the only subroutine it needs is Cholesky factorization, … Read more

    Global Optimization in Hilbert Space

  • Benoit Chachuat
  • Boris Houska
    • Categories Global Optimization Theory, Infinite Dimensional Optimization

    This paper proposes a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. … Read more

    Decomposition-Based Approximation Algorithms for the One-Warehouse Multi-Retailer Problem with Concave Batch Order Costs

  • Maged M. Dessouky
  • Weihong Hu
  • Alejandro Toriello
  • Zhuoting Yu
    • Categories Approximation Algorithms, Production and Logistics, Supply Chain Management Tags , ,

    We study the one-warehouse multi-retailer (OWMR) problem under deterministic dynamic demand and concave batch order costs, where order batches have an identical capacity and the order cost function for each facility is concave within the batch. Under appropriate assumptions on holding cost structure, we obtain lower bounds via a decomposition that splits the two-echelon problem … Read more

    A Benders decomposition based framework for solving cable trench problems

  • Hatice Calik
  • Markus Leitner
  • Martin Luipersbeck
    • Categories Integer Programming, Network Optimization Tags , , ,

    In this work, we present an algorithmic framework based on Benders decomposition for the Capacitated p-Cable Trench Problem with Covering. We show that our approach can be applied to most variants of the Cable Trench Problem (CTP) that have been considered in the literature. The proposed algorithm is augmented with a stabilization procedure to accelerate … Read more

    A new branch-and-bound algorithm for standard quadratic programming problems

  • Giampaolo Liuzzi
  • Marco Locatelli
  • Veronica Piccialli
    • Categories Global Optimization, Quadratic Programming

    In this paper we propose convex and LP bounds for Standard Quadratic Programming (StQP) problems and employ them within a branch-and-bound approach. We first compare different bounding strategies for StQPs in terms both of the quality of the bound and of the computation times. It turns out that the polyhedral bounding strategy is the best … Read more

    Improving Benders decomposition via a non-linear cut selection procedure

  • R.S. Camargo
  • F. M. S. Lima
  • G. Miranda
    • Categories Applications - OR and Management Sciences, Cutting Plane Approaches, Network Optimization

    A non-linear lifting procedure is proposed to generate high density Benders cuts. The new denser cuts cover more master problem variables than traditional Benders cuts, shortening the required number of iterations to reach optimality, and speeding up the Benders decomposition algorithm. To lessen the intricacy stemmed from the non-linearity, a simple outer approximation lineariza- tion … Read more

    Formulations and Decomposition Methods for the Incomplete Hub Location Problem With and Without Hop-Constraints

  • R.S. Camargo
  • J. F. Campbell
  • Gilberto Miranda
  • M. E. O' Kelly
    • Categories Airline Optimization, Applications - OR and Management Sciences, Transportation Tags , , , ,

    The incomplete hub location problem with and without hop-constraints is modeled using a Leontief substitution system approach. The Leontief formalism provides a set of important theoretical properties and delivers formulations with tight linear bounds that can explicitly incorporate hop constraints for each origin-destination pair of demands. Furthermore, the proposed formulations are amenable to a Benders … Read more

    Asymptotical Analysis of a SAA Estimator for Optimal Value of a Two Stage Problem with Quadratic Recourse

  • Qingsong Duan
  • Liwei Zhang
  • Hongwei Zhang
  • Sainan Zhang
    • Categories Quadratic Programming, Stochastic Programming Tags , , , ,

    In this paper, we first consider the stability analysis of a convex quadratic programming problem and its restricted Wolfe dual in which all parameters in the problem are perturbed. We demonstrate the upper semi-continuity of solution mappings for the primal problem and the restricted Wolfe dual problem and establish the Hadamard directionally differentiability of the … Read more