A Regularized Smoothing Method for Fully Parameterized Convex Problems with Applications to Convex and Nonconvex Two-Stage Stochastic Programming

  • Pedro Borges de Melo
  • Claudia Sagastizábal
  • Mikhail V. Solodov
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    We present an approach to regularize and approximate solution mappings of parametric convex optimization problems that combines interior penalty (log-barrier) solutions with Tikhonov regularization. Because the regularized mappings are single-valued and smooth under reasonable conditions, they can be used to build a computationally practical smoothing for the associated optimal value function. The value function in … Read more

    Risk-Neutral and Risk-Averse Transmission Switching for Load Shed Recovery

  • Manish Bansal
  • Adolfo Escobedo
  • Yingqiu Zhang
    • Categories Applications - OR and Management Sciences, Energy, Stochastic Programming Tags , , ,

    Maintaining an uninterrupted supply of electricity is a fundamental goal of power systems operators. However, due to critical outage events, customer demand or load is at times disconnected or shed temporarily. While deterministic optimization models have been devised to help operators expedite load shed recovery by harnessing the flexibility of the grid’s topology (i.e., transmission … Read more

    Dynamic programming for the time-dependent traveling salesman problem with time windows

  • Gonzalo Lera-Romero
  • Juan JosĂ© Miranda-Bront
  • Francisco J. Soulignac
    • Categories Dynamic Programming, Transportation Tags , , , , ,

    The recent growth of direct-to-consumer deliveries has stressed the importance of last-mile logistics, becoming one of the critical factors in city planning. One of the key factors lies in the last-mile deliveries, reaching in some cases nearly 50% of the overall parcel delivery cost. Different variants of the the well-known Traveling Salesman Problem (TSP) arise … Read more

    On the acceleration of the Barzilai-Borwein method

  • Yu-Hong Dai
  • Yakui Huang
  • Xin-Wei Liu
  • Hongchao Zhang
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization

    The Barzilai-Borwein (BB) gradient method is efficient for solving large-scale unconstrained problems to the modest accuracy and has a great advantage of being easily extended to solve a wide class of constrained optimization problems. In this paper, we propose a new stepsize to accelerate the BB method by requiring finite termination for minimizing two-dimensional strongly … Read more

    Exact semidefinite programming bounds for packing problems

  • David de Laat
  • Maria Dostert
  • Philippe Moustrou
    • Categories Semi-definite Programming Tags ,

    In this paper we give an algorithm to round the floating point output of a semidefinite programming solver to a solution over the rationals or a quadratic extension of the rationals. We apply this to get sharp bounds for packing problems, and we use these sharp bounds to prove that certain optimal packing configurations are … Read more

    Achieving Consistency with Cutting Planes

  • Danial Davarnia
  • Atefeh Rajabalizadeh
  • John Hooker
    • Categories 0-1 Programming, Cutting Plane Approaches Tags , , , ,

    Cutting planes accelerate branch-and-bound search primarily by cutting off fractional solutions of the linear programming (LP) relaxation, resulting in tighter bounds for pruning the search tree. Yet cutting planes can also reduce backtracking by excluding inconsistent partial assignments that occur in the course of branching. A partial assignment is inconsistent with a constraint set when … Read more

    Data-Driven Two-Stage Conic Optimization with Zero-One Uncertainties

  • Mohamed El Tonbari
  • Kibaek Kim
  • Anirudh Subramanyam
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications. Given a sparse training dataset of the parameters, we motivate and study a distributionally robust formulation of the problem using a Wasserstein ambiguity set centered at … Read more

    Lossless Compression of Deep Neural Networks

  • Abhinav Kumar
  • Srikumar Ramalingam
  • Thiago Serra
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering

    Deep neural networks have been successful in many predictive modeling tasks, such as image and language recognition, where large neural networks are often used to obtain good accuracy. Consequently, it is challenging to deploy these networks under limited computational resources, such as in mobile devices. In this work, we introduce an algorithm that removes units … Read more

    Stochastic Dual Dynamic Programming for Multistage Stochastic Mixed-Integer Nonlinear Optimization

  • Shixuan Zhang
  • Xu Andy Sun
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Stochastic Programming Tags , , ,

    In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with \emph{non-Lipschitz-continuous} value functions and multistage stochastic mixed-integer linear optimization. We develop stochastic dual dynamic programming (SDDP) type algorithms with nested decomposition, deterministic sampling, and stochastic sampling. The key ingredient … Read more

    Joint Pricing and Production: A Fusion of Machine Learning and Robust Optimization

  • Georgia Perakis
  • Qinshen Tang
  • Peng Xiong
  • Melvyn Sim
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    We integrate machine learning with distributionally robust optimization to address a two-period problem for the joint pricing and production of multiple items. First, we generalize the additive demand model to capture both cross-product and cross-period effects as well as the demand dependence across periods. Next, we apply K-means clustering to the demand residual mapping based … Read more