An Accelerated Inexact Dampened Augmented Lagrangian Method for Linearly-Constrained Nonconvex Composite Optimization Problems

  • Weiwei Kong
  • Renato D.C. Monteiro
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    This paper proposes and analyzes an accelerated inexact dampened augmented Lagrangian (AIDAL) method for solving linearly-constrained nonconvex composite optimization problems. Each iteration of the AIDAL method consists of: (i) inexactly solving a dampened proximal augmented Lagrangian (AL) subproblem by calling an accelerated composite gradient (ACG) subroutine; (ii) applying a dampened and under-relaxed Lagrange multiplier update; … Read more

    A Preconditioned Iterative Interior Point Approach to the Conic Bundle Subproblem

  • Christoph Helmberg
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    The conic bundle implementation of the spectral bundle method for large scale semidefinite programming solves in each iteration a semidefinite quadratic subproblem by an interior point approach. For larger cutting model sizes the limiting operation is collecting and factorizing a Schur complement of the primal-dual KKT system. We explore possibilities to improve on this by … Read more

    A Graph-based Decomposition Method for Convex Quadratic Optimization with Indicators

  • Peijing Liu
  • Salar Fattahi
  • Andrés Gómez
  • Simge Küçükyavuz
    • Categories (Mixed) Integer Nonlinear Programming, Statistics Tags , , , , , ,

    In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix Q defining the quadratic term in the objective is sparse. We use a graphical representation of the support of Q, and show that if this graph is a path, then we can solve the associated problem in polynomial time. This … Read more

    Distributionally Favorable Optimization: A Framework for Data-driven Decision-making with Endogenous Outliers

  • Nan Jiang
  • Weijun Xie
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    A typical data-driven stochastic program aims to seek the best decision that minimizes the sum of a deterministic cost function and an expected recourse function under a given distribution. Recently, much success has been witnessed in the development of Distributionally Robust Optimization (DRO), which considers the worst-case expected recourse function under the least favorable probability … Read more

    A Branch & Bound Algorithm for Robust Binary Optimization with Budget Uncertainty

  • Christina Büsing
  • Timo Gersing
  • Arie M.C.A. Koster
    • Categories 0-1 Programming, Branch and Cut Algorithms, Robust Optimization Tags , , , ,

    Since its introduction in the early 2000s, robust optimization with budget uncertainty has received a lot of attention. This is due to the intuitive construction of the uncertainty sets and the existence of a compact robust reformulation for (mixed-integer) linear programs. However, despite its compactness, the reformulation performs poorly when solving robust integer problems due … Read more

    ADMM-based Unit and Time Decomposition for Price Arbitrage by Cooperative Price-Maker Electricity Storage Units

  • Miguel F. Anjos
  • James Cruise
  • Albert Solà Vilalta
    • Categories Convex Optimization, Dynamic Programming, Energy Tags , , , , , , ,

    Decarbonization via the integration of renewables poses significant challenges for electric power systems, but also creates new market opportunities. Electric energy storage can take advantage of these opportunities while providing flexibility to power systems that can help address these challenges. We propose a solution method for the optimal control of multiple price-maker electric energy storage … Read more

    An Overview of Nested Decomposition for Multi-Level Optimization Problems

  • Stephen J. Maher
  • Ibrahim Muter
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Integer Programming Tags , , , ,

    Nested multi-level structures are frequently encountered in many real-world optimization problems. Decomposition techniques are a commonly applied approach used to handle nested multi-level structures; however, the typical problem-specific focus of such techniques has led to numerous specialized formulations and solution methods. This lack of generalized results for nested multi-level optimization problems is addressed in this … Read more

    Efficient and Robust Mixed-Integer Optimization Methods for Training Binarized Deep Neural Networks

  • Jannis Kurtz
  • Bubacarr Bah
    • Categories Applications - OR and Management Sciences, Integer Programming, Robust Optimization Tags ,

    Compared to classical deep neural networks its binarized versions can be useful for applications on resource-limited devices due to their reduction in memory consumption and computational demands. In this work we study deep neural networks with binary activation functions and continuous or integer weights (BDNN). We show that the BDNN can be reformulated as a … Read more

    Differential Privacy in Multi-Party Resource Sharing

  • Utku Karaca
  • Ş. İlker Birbil
  • Nursen Aydin
  • Gizem Mullaoğlu
  • Sinan Yıldırım
    • Categories Applications - OR and Management Sciences Tags , , ,

    This study examines a resource-sharing problem involving multiple parties that agree to use a set of capacities together. We start with modeling the whole problem as a mathematical program, where all parties are required to exchange information to obtain the optimal objective function value. This information bears private data from each party in terms of … Read more

    Exact computation of an error bound for a generalized linear complementarity problem with unique solution

  • Jean-Pierre Dussault
  • Jean Charles Gilbert
    • Categories Complementarity and Variational Inequalities Tags , , , , , , , , ,

    This paper considers a generalized form of the standard linear complementarity problem with unique solution and provides a more precise expression of an upper error bound discovered by Chen and Xiang in 2006. This expression has at least two advantages. It makes possible the exact computation of the error bound factor and it provides a … Read more