Applications – Science and Engineering

Per-RMAP: Feasibility-Seeking and Superiorization Methods for Floorplanning with I/O Assignment

  • ShanYu
  • Yair Censor
  • Ming Jiang
  • Guojie Luo
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, VLSI layout Tags , , , ,

    The feasibility-seeking approach provides a systematic scheme to manage and solve complex constraints for continuous problems, and we explore it for the floorplanning problems with increasingly heterogeneous constraints. The classic legality constraints can be formulated as the union of convex sets. However, the convergence of conventional projection-based algorithms is not guaranteed when the constraints sets … Read more

    Polynomial argmin for recovery and approximation of multivariate discontinuous functions

  • Didier Henrion
  • Milan Korda
  • Jean-Bernard Lasserre
    • Categories Basic Sciences Applications, Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , ,

    We propose to approximate a (possibly discontinuous) multivariate function f(x) on a compact set by the partial minimizer arg min_y p(x,y) of an appropriate polynomial p whose construction can be cast in a univariate sum of squares (SOS) framework, resulting in a highly structured convex semidefinite program. In a number of non-trivial cases (e.g. when … Read more

    Bilevel optimization with a multi-objective lower-level problem: Risk-neutral and risk-averse formulations

  • Tommaso Giovannelli
  • Griffin D. Kent
  • Luis Nunes Vicente
    • Categories Data-Mining, Multi-Criteria Optimization, Stochastic Programming Tags , , ,

    In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the deterministic case and have never been studied from a stochastic approximation viewpoint despite the recent advances in stochastic methods for single-level, bilevel, and multi-objective … Read more

    MGProx: A nonsmooth multigrid proximal gradient method with adaptive restriction for strongly convex optimization

  • Andersen Ang
  • Stephen A. Vavasis
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization, Nonlinear Optimization

    We study the combination of proximal gradient descent with multigrid for solving a class of possibly nonsmooth strongly convex optimization problems. We propose a multigrid proximal gradient method called MG-Prox, which accelerates the proximal gradient method by multigrid, based on using hierarchical information of the optimization problem. MGProx applies a newly introduced adaptive restriction operator … Read more

    Force-Controlled Pose Optimization and Trajectory Planning for Chained Stewart Platforms

  • William Chapin
  • Samantha Chapin
  • Robert Hildebrand
    • Categories Global Optimization, Mechanical Engineering, Quadratic Programming

    We study optimization methods applied to minimizing forces for poses and movements of chained Stewart platforms (SPs) that we call an “Assembler” Robot. These chained SPs are parallel mechanisms that are stronger, stiffer, and more precise, on average, than their serial counterparts at the cost of a smaller range of motion. Linking these units in … Read more

    Gas Transport Network Optimization: PDE-Constrained Models

  • Falk M. Hante
  • Martin Schmidt
    • Categories Applications - Science and Engineering, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    The optimal control of gas transport networks was and still is a very important topic for modern economies and societies. Accordingly, a lot of research has been carried out on this topic during the last years and decades. Besides mixed-integer aspects in gas transport network optimization, one of the main challenges is that a physically … Read more

    Gas Transport Network Optimization: Mixed-Integer Nonlinear Models

  • Falk M. Hante
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering Tags , , ,

    Although modern societies strive towards energy systems that are entirely based on renewable energy carriers, natural gas is still one of the most important energy sources. This became even more obvious in Europe with Russia’s 2022 war against the Ukraine and the resulting stop of gas supplies from Russia. Besides that it is very important … Read more

    The min-Knapsack Problem with Compactness Constraints and Applications in Statistics

  • Alberto Santini
  • Enrico Malaguti
    • Categories Branch and Cut Algorithms, Dynamic Programming, Statistics Tags , ,

    In the min-Knapsack problem, one is given a set of items, each having a certain cost and weight. The objective is to select a subset with minimum cost, such that the sum of the weights is not smaller than a given constant. In this paper we introduce an extension of the min-Knapsack problem with additional … Read more

    Superiorization: The asymmetric roles of feasibility-seeking and objective function reduction

  • Yair Censor
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , , , , ,

    The superiorization methodology can be thought of as lying conceptually between feasibility-seeking and constrained minimization. It is not trying to solve the full-fledged constrained minimization problem composed from the modeling constraints and the chosen objective function. Rather, the task is to find a feasible point which is “superior” (in a well-defined manner) with respect to … Read more

    Optimization of the first Dirichlet Laplacian eigenvalue with respect to a union of balls

  • Ernesto G. Birgin
  • Lucas Fernandez
  • Gabriel Haeser
  • Antoine
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs Tags , ,

    The problem of minimizing the first eigenvalue of the Dirichlet Laplacian with respect to a union of m balls with fixed identical radii and variable centers in the plane is investigated in the present work. The existence of a minimizer is shown and the shape sensitivity analysis of the eigenvalue with respect to the centers’ … Read more