Month: April 2025

A Survey on the Applications of Stochastic Dual Dynamic Programming and its Variants

  • Bonn Kleiford Seranilla
  • Nils Löhndorf
    • Categories Dynamic Programming, Integer Programming, Stochastic Programming Tags , , ,

    Stochastic Dual Dynamic Programming (SDDP) is widely recognized as the predominant methodology for solving large-scale multistage stochastic linear programming (MSLP) problems. This paper aims to contribute to the extant literature by conducting a comprehensive survey of the literature on SDDP within the realm of practical applications. We systematically identify and analyze the various domains where … Read more

    Deterministic global optimization with trained neural networks: Is the envelope of single neurons worth it?

  • Clara Witte
  • Jannik Lüthje
  • Victor Schulte
  • Alexander Mitsos
  • Dominik Bongartz
    • Categories Global Optimization, Global Optimization Applications, Optimization in Data Science Tags , , ,

    Optimization problems containing trained neural networks remain challenging due to their nonconvexity. Deterministic global optimization relies on relaxations which should be tight, quickly convergent, and cheap to evaluate. While envelopes of common activation functions have been established for several years, the envelope of an entire neuron had not. Recently, Carrasco and Mu\~{n}oz (arXiv.2410.23362, 2024) proposed … Read more

    The improvement function in branch-and-bound methods for complete global optimization

  • Stefan Schwarze
  • Oliver Stein
  • Peter Kirst
    • Categories Constrained Nonlinear Optimization, Global Optimization Tags , , , ,

    We present a new spatial branch-and-bound approach for treating optimization problems with nonconvex inequality constraints. It is able to approximate the set of all global minimal points in case of solvability, and else to detect infeasibility. The new technique covers the nonconvex constraints by means of an improvement function which, although nonsmooth, can be treated … Read more

    IPAS: An Adaptive Sample Size Method for Weighted Finite Sum Problems with Linear Equality Constraints

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Sanja Rapajić
  • Luka Rutešić
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic optimization method is proposed. The method belongs to the class of variable sample size first order methods, … Read more

    Strong Formulations and Algorithms for Regularized A-Optimal Design

  • Yongchun Li
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization Tags , , , ,

    We study the Regularized A-Optimal Design (RAOD) problem, which selects a subset of \(k\) experiments to minimize the inverse of the Fisher information matrix, regularized with a scaled identity matrix. RAOD has broad applications in Bayesian experimental design, sensor placement, and cold-start recommendation. We prove its NP-hardness via a reduction from the independent set problem. … Read more

    Time Complexity and Optimality of Inventory and Production Policies for a Dynamic Lot Sizing Model with Remanufacturing and Separate Setup Costs

  • Chee-Khian Sim
    • Categories Dynamic Programming, Production and Logistics Tags , , ,

    In this paper, we consider a dynamic lot sizing model with remanufacturing having m types of cores. The model also allows manufacturing. We consider separate setup costs for manufacturing and remanufacturing in our model. It is conjectured in [15], with reference to [18], that finding an optimal policy to the model when there is separate … Read more

    The Undirected Team Orienteering Arc Routing Problem: Formulations, Valid Inequalities, and Exact Algorithms

  • Wenjin Yan
  • Elena Fernandez
  • Ivana Ljubić
    • Categories Branch and Cut Algorithms, Combinatorial Optimization, Network Optimization Tags , , ,

    We address the Undirected Team Orienteering Arc Routing Problem (UTOARP). In this problem, demand is placed at some edges of a given undirected graph and served demand edges produce a profit. Feasible routes must start and end at a given depot and there is a time limit constraint on the maximum duration of each route. … Read more

    The improvement function reformulation for graphs of minimal point mappings

  • Stefan Schwarze
  • Oliver Stein
    • Categories Constrained Nonlinear Optimization, Game Theory, Global Optimization Theory Tags , , , , ,

    Graphs of minimal point mappings of parametric optimization problems appear in the definition of feasible sets of bilevel optimization problems and of semi-infinite optimization problems, and the intersection of multiple such graphs defines (generalized) Nash equilibria. This paper shows how minimal point graphs of nonconvex parametric optimization problems can be written with the help of … Read more

    Rank-one convexification for convex quadratic optimization with step function penalties

  • Andrés Gómez
  • Shaoning Han
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Applications, Semi-definite Programming Tags ,

    We investigate convexification in convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step function. First, we derive the convex hull for the epigraph of a quadratic function defined by a rank-one matrix. Using this rank-one convexification, we … Read more

    A Foundational Perspective for Partitional Clustering on Networks

  • Derya Ipek Eroglu
  • Cem Iyigun
    • Categories Data Science Theory, Data-Mining, Optimization in Data Science Tags , , ,

    This study presents a theoretical analysis of partitional clustering on networks. Different versions of the problem are studied considering different assignment schemes (hard and soft) and different objective functions. Cluster centers are not restricted to only the set of nodes, it is assumed that centers can also be at the edges of the network. Four … Read more