Infinite Dimensional Optimization

Minimum weight Topology optimization subject to unsteady heat equation and space-time pointwise constraints — toward automatic optimal riser design in the shape casting process

  • Rouhollah Tavakoli
    • Categories Distributed Control, Mechanical Engineering, Multidisciplinary Design Optimization Tags , , , , ,

    The automatic optimal design of feeding system in the shape casting process is considered in the present work. In fact, the goal is to find the optimal position, size, shape and topology of risers in the shape casting process. This problem is formulated as a minimum weight topology optimization problem subjected to a nonlinear transient … Read more

    New formulas for the Fenchel subdifferential of the conjugate function

  • Rafael Correa
  • Abderrahim Hantoute
    • Categories Convex and Nonsmooth Optimization, Infinite Dimensional Optimization Tags , , ,

    Following [13] we provide new formulas for the Fenchel subdifferential of the conjugate of functions defined on locally convex spaces. In particular, this allows deriving expressions for the minimizers set of the lower semicontinuous convex hull of such functions. These formulas are written by means of primal objects related to the subdifferential of the initial … Read more

    Solving Infinite-dimensional Optimization Problems by Polynomial Approximation

  • Olivier Devolder
  • François Glineur
  • Yurii Nesterov
    • Categories Convex Optimization, Infinite Dimensional Optimization Tags , , , , , ,

    We solve a class of convex infinite-dimensional optimization problems using a numerical approximation method that does not rely on discretization. Instead, we restrict the decision variable to a sequence of finite-dimensional linear subspaces of the original infinite-dimensional space and solve the corresponding finite-dimensional problems in a efficient way using structured convex optimization techniques. We prove … Read more

    Double smoothing technique for infinite-dimensional optimization problems with applications to Optimal Control.

  • Olivier Devolder
  • François Glineur
  • Yurii Nesterov
    • Categories Convex Optimization, Infinite Dimensional Optimization Tags , , , ,

    In this paper, we propose an efficient technique for solving some infinite-dimensional problems over the sets of functions of time. In our problem, besides the convex point-wise constraints on state variables, we have convex coupling constraints with finite-dimensional image. Hence, we can formulate a finite-dimensional dual problem, which can be solved by efficient gradient methods. … Read more

    Implicit Multifunction Theorems in complete metric spaces

  • Van Ngai Huynh
  • Huu Tron Nguyen
  • Michel Thera
    • Categories Infinite Dimensional Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper, we establish some new characterizations of the metric regularity of implicit multifunctions in complete metric spaces by using the lower semicontinuous envelopes of the distance functions for set-valued mappings. Through these new characterizations it is possible to investigate implicit multifunction theorems based on coderivatives and on contingent derivatives as well as the … Read more

    Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions

  • Samir Adly
  • Abderrahim Hantoute
  • Michel Thera
    • Categories Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , , , ,

    The main objective of this paper is to provide new explicit criteria to characterize weak lower semi-continuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by the means of the proximal … Read more

    Combinatorial Integral Approximation

  • Michael N. Jung
  • Christian Kirches
  • Sebastian Sager
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Distributed Control Tags , ,

    We are interested in structures and efficient methods for mixed-integer nonlinear programs (MINLP) that arise from a first discretize, then optimize approach to time-dependent mixed-integer optimal control problems (MIOCPs). In this study we focus on combinatorial constraints, in particular on restrictions on the number of switches on a fixed time grid. We propose a novel … Read more

    Lipschitz solutions of optimal control problems with state constraints of arbitrary order

  • Joseph Frédéric Bonnans
    • Categories Control Applications, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , ,

    In this paper we generalize to an arbitrary order, under minimal hypotheses, some sufficient conditions for Lipschitz continuity of the solution of a state constrained optimal control problems. The proof combines the approach by Hager in 1979 for dealing with first-order state constraints, and the high-order alternative formulation of the optimality conditions. CitationPublished as INRIA … Read more

    A continuous model for open pit mine planning

  • Felipe Álvarez
  • Andreas Griewank
  • Jorge Amaya
  • Nikolai Strogies
    • Categories Applications - OR and Management Sciences, Global Optimization, Infinite Dimensional Optimization Tags , ,

    This paper proposes a new mathematical model for the open pit mine planning problem, based on continuous functional analysis. The traditional models for this problem have been constructed by using discrete 0-1 decision variables, giving rise to large-scale combinatorial and Mixed Integer Programming (MIP) problems. Instead, we use a continuous approach which allows for a … Read more