An adaptive regularization algorithm for unconstrained optimization with inexact function and derivatives values

  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , ,

    An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In comparison with a similar algorithm proposed in Cartis, Gould, Toint (2022), its distinguishing feature is that it is based on controlling the relative error between … Read more

    Trust-region algorithms: probabilistic complexity and intrinsic noise with applications to subsampling techniques

  • Stefania Bellavia
  • Gianmarco Gurioli
  • Benedetta Morini
  • Philippe L. Toint
    • Categories Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , , , ,

    A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method finds (in expectation) an epsilon-approximate minimizer of arbitrary order q > 0 in at most O(epsilon^{-(q+1)}) inexact evaluations of the function and … Read more

    Risk-averse Regret Minimization in Multi-stage Stochastic Programs

  • Mehran Poursoltani
  • Erick Delage
  • Angelos Georghiou
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , ,

    Within the context of optimization under uncertainty, a well-known alternative to minimizing expected value or the worst-case scenario consists in minimizing regret. In a multi-stage stochastic programming setting with a discrete probability distribution, we explore the idea of risk-averse regret minimization, where the benchmark policy can only benefit from foreseeing Delta steps into the future. … Read more

    Multiple-Periods Locally-Facet-Based MIP Formulations for the Unit Commitment Problem

  • Linfeng Yang
  • Shifei Chen
  • Zhaoyang Dong
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Polyhedra Tags , , , , , , ,

    The thermal unit commitment (UC) problem has historically been formulated as a mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale systems. The tighter characteristic reduces the search space, therefore, as a natural consequence, significantly reduces the computational burden. In literatures, many tightened formulations for a single unit with parts … Read more

    OPM, a collection of Optimization Problems in Matlab

  • Serge Gratton
  • Philippe L. Toint
    • Categories Bound-constrained Optimization, Optimization Software Benchmark, Unconstrained Optimization Tags , , ,

    OPM is a small collection of CUTEst unconstrained and bound-constrained nonlinear optimization problems, which can be used in Matlab for testing optimization algorithms directly (i.e. without installing additional software). Article Download View OPM, a collection of Optimization Problems in Matlab

    The Value of Robust Assortment Optimization Under Ranking-based Choice Models

  • Bradley Sturt
    • Categories Marketing, Robust Optimization, Yield Management Tags , ,

    We study a class of robust assortment optimization problems that was proposed by Farias, Jagabathula, and Shah (2013). The goal in these problems is to find an assortment that maximizes a firm’s worst-case expected revenue under all ranking-based choice models that are consistent with the historical sales data generated by the firm’s past assortments. We … Read more

    A Finitely Convergent Cutting Plane, and a Bender’s Decomposition Algorithm for Mixed-Integer Convex and Two-Stage Convex Programs using Cutting Planes

  • Fengqiao Luo
  • Sanjay Mehrotra
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Stochastic Programming Tags , , ,

    We consider a general mixed-integer convex program. We first develop an algorithm for solving this problem, and show its nite convergence. We then develop a finitely convergent decomposition algorithm that separates binary variables from integer and continuous variables. The integer and continuous variables are treated as second stage variables. An oracle for generating a parametric … Read more

    Robust Concave Utility Maximization over Chance Constraints

  • Shanshan Wang
  • Sanjay Mehrotra
  • Chun Peng
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , , , ,

    This paper first studies an expected utility problem with chance constraints and incomplete information on a decision maker’s utility function. The model maximizes the worst-case expected utility of random outcome over a set of concave functions within a novel ambiguity set, while the underlying probability distribution is known. To obtain computationally tractable formulations, we employ … Read more

    Tractable Robust Supervised Learning Models

  • Melvyn Sim
  • Long Zhao
  • Minglong Zhou
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    At the heart of supervised learning is a minimization problem with an objective function that evaluates a set of training data over a loss function that penalizes poor fitting and a regularization function that penalizes over-fitting to the training data. More recently, data-driven robust optimization based learning models provide an intuitive robustness perspective of regularization. … Read more

    Lower bound on size of branch-and-bound trees for solving lot-sizing problem

  • Santanu S. Dey
  • Prachi Shah
    • Categories 0-1 Programming, Integer Programming Tags , ,

    We show that there exists a family of instances of the lot-sizing problem, such that any branch-and-bound tree that solves them requires an exponential number of nodes, even in the case when the branchings are performed on general split disjunctions. Article Download View Lower bound on size of branch-and-bound trees for solving lot-sizing problem