Optimization Software and Modeling Systems

An improved randomized algorithm with noise level tuning for large-scale noisy unconstrained DFO problems

  • Morteza Kimiaei
    • Categories Optimization Software Benchmark, Stochastic Programming, Unconstrained Optimization Tags , , , ,

    In this paper, a new randomized solver (called VRDFON) for noisy unconstrained derivative-free optimization (DFO) problems is discussed. Complexity result in the presence of noise for nonconvex functions is studied. Two effective ingredients of VRDFON are an improved derivative-free line search algorithm with many heuristic enhancements and quadratic models in adaptively determined subspaces. Numerical results … Read more

    Limited-memory Common-directions Method for Large-scale Optimization: Convergence, Parallelization, and Distributed Optimization

  • Ching-pei Lee
  • Po-Wei Wang
  • Chih-Jen Lin
    • Categories Parallel Algorithms, Unconstrained Optimization Tags , , ,

    In this paper, we present a limited-memory common-directions method for smooth optimization that interpolates between first- and second- order methods. At each iteration, a subspace of a limited dimension size is constructed using first-order information from previous iterations, and an ef- ficient Newton method is deployed to find an approximate minimizer within this subspace. With … Read more

    A Two-level ADMM Algorithm for AC OPF with Convergence Guarantees

  • Xu Andy Sun
  • Kaizhao Sun
    • Categories Constrained Nonlinear Optimization, Network Optimization, Parallel Algorithms Tags , , ,

    This paper proposes a two-level distributed algorithmic framework for solving the AC optimal power flow (OPF) problem with convergence guarantees. The presence of highly nonconvex constraints in OPF poses significant challenges to distributed algorithms based on the alternating direction method of multipliers (ADMM). In particular, convergence is not provably guaranteed for nonconvex network optimization problems … Read more

    The confined primal integral

  • Timo Berthold
  • Zsolt Csizmadia
    • Categories (Mixed) Integer Nonlinear Programming, Optimization Software Benchmark Tags , ,

    It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and … Read more

    ROC++: Robust Optimization in C++

  • Phebe Vayanos
  • Qing Jin
  • George Elissaios
    • Categories Optimization Software and Modeling Systems, Robust Optimization Tags , , , , , ,

    Over the last two decades, robust optimization has emerged as a popular means to address decision-making problems affected by uncertainty. This includes single- and multi-stage problems involving real-valued and/or binary decisions, and affected by exogenous (decision-independent) and/or endogenous (decision-dependent) uncertain parameters. Robust optimization techniques rely on duality theory potentially augmented with approximations to transform a … Read more

    Manifold Identification for Ultimately Communication-Efficient Distributed Optimization

  • Wei-Lin Chiang
  • Yu-Sheng Li
  • Ching-pei Lee
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Parallel Algorithms Tags , , ,

    This work proposes a progressive manifold identification approach for distributed optimization with sound theoretical justifications to greatly reduce both the rounds of communication and the bytes communicated per round for partly-smooth regularized problems such as the $\ell_1$- and group-LASSO-regularized ones. Our two-stage method first uses an inexact proximal quasi-Newton method to iteratively identify a sequence … Read more

    A Restricted Dual Peaceman-Rachford Splitting Method for QAP

  • Naomi Graham
  • Hao Hu
  • Xinxin Li
  • Henry Wolkowicz
  • Haesol Im
    • Categories (Mixed) Integer Nonlinear Programming, Linear, Cone and Semidefinite Programming, Optimization Software Benchmark Tags , , , ,

    We revisit and strengthen splitting methods for solving doubly nonnegative, DNN, relaxations of the quadratic assignment problem, QAP. We use a modified restricted contractive splitting method, rPRSM, approach. Our strengthened bounds and new dual multiplier estimates improve on the bounds and convergence results in the literature. Citation Department of Combinatorics & Optimization, University of Waterloo, … Read more

    Solving Previously Unsolved MIP Instances with ParaSCIP on Supercomputers by using up to 80,000 Cores

  • Tobias Achterberg
  • Timo Berthold
  • Stefan Heinz
  • Thorsten Koch
  • Yuji Shinano
  • Michael Winkler
    • Categories (Mixed) Integer Linear Programming, Parallel Algorithms, Problem Solving Environments Tags , , , , , ,

    Mixed-integer programming (MIP) problem is arguably among the hardest classes of optimization problems. This paper describes how we solved 21 previously unsolved MIP instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in … Read more

    Linearization and Parallelization Schemes for Convex Mixed-Integer Nonlinear Optimization

  • Meenarli Sharma
  • Prashant Palkar
  • Ashutosh Mahajan
    • Categories (Mixed) Integer Nonlinear Programming, Parallel Algorithms Tags , , , ,

    We develop and test linearization and parallelization schemes for convex mixed-integer nonlinear programming. Several linearization approaches are proposed for LP/NLP based branch-and-bound. Some of these approaches strengthen the linear approximation to nonlinear constraints at the root node and some at the other branch-and-bound nodes. Two of the techniques are specifically applicable to commonly found univariate … Read more

    Towards practical generic conic optimization

  • Chris Coey
  • Juan Pablo Vielma
  • Lea Kapelevich
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , ,

    Many convex optimization problems can be represented through conic extended formulations with auxiliary variables and constraints using only the small number of standard cones recognized by advanced conic solvers such as MOSEK 9. Such extended formulations are often significantly larger and more complex than equivalent conic natural formulations, which can use a much broader class … Read more