Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems with Mixed Two-Point Boundary Conditions

  • Richard Krug
  • Günter Leugering
  • Martin Schmidt
  • Dieter Weninger
  • Alexander Martin
    • Categories Systems governed by Differential Equations Optimization Tags , , , ,

    In this article, we continue our work (Krug et al., 2021) on time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations in that we now consider mixed two-point boundary value problems and provide an in-depth well-posedness analysis. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems … Read more

    What is the optimal cutoff surface for ore bodies with more than one mineral?

  • Lewis Ntaimo
  • Bernardo K. Pagnoncelli
  • A. Piazza
    • Categories Applications - OR and Management Sciences, Control Applications, Dynamic Programming

    In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution … Read more

    First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition

  • Roberto Andreani
  • Gabriel Haeser
  • Héctor Ramírez
  • Leonardo M. Mito
  • Thiago P. Siqueira
    • Categories Constrained Nonlinear Optimization, Second-Order Cone Programming, Semi-definite Programming

    The well known constant rank constraint qualification [Math. Program. Study 21:110–126, 1984] introduced by Janin for nonlinear programming has been recently extended to a conic context by exploiting the eigenvector structure of the problem. In this paper we propose a more general and geometric approach for defining a new extension of this condition to the … Read more

    An extension of the Reformulation-Linearization Technique to nonlinear optimization

  • Danique de Moor
  • Dick den Hertog
  • Jianzhe Zhen
    • Categories Constrained Nonlinear Optimization, Global Optimization Tags , , ,

    We introduce a novel Reformulation-Perspectification Technique (RPT) to obtain convex approximations of nonconvex continuous optimization problems. RPT consists of two steps, those are, a reformulation step and a perspectification step. The reformulation step generates redundant nonconvex constraints from pairwise multiplication of the existing constraints. The perspectification step then convexifies the nonconvex components by using perspective … Read more

    The Promise of EV-Aware Multi-Period OPF Problem: Cost and Emission Benefits

  • Sezen Ece Kayacık
  • Burak Kocuk
  • Tuğçe Yüksel
    • Categories Applications - OR and Management Sciences, Global Optimization, Second-Order Cone Programming Tags , ,

    In this paper, we study the Multi-Period Optimal Power Flow problem (MOPF) with electric vehicles (EV) under emission considerations. We integrate three different real-world datasets: household electricity consumption, marginal emission factors, and EV driving profiles. We present a systematic solution approach based on second-order cone programming to find globally optimal solutions for the resulting nonconvex … Read more

    Quantifying uncertainty with ensembles of surrogates for blackbox optimization

  • Charles Audet
  • Sébastien Le Digabel
  • Renaud Saltet
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    This work is in the context of blackbox optimization where the functions defining the problem are expensive to evaluate and where no derivatives are available. A tried and tested technique is to build surrogates of the objective and the constraints in order to conduct the optimization at a cheaper computational cost. This work proposes different … Read more

    Regularized quasi-monotone method for stochastic optimization

  • Vyacheslav Kungurtsev
  • Vladimir Shikhman
    • Categories Convex and Nonsmooth Optimization

    We adapt the quasi-monotone method from Nesterov, Shikhman (2015) for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is standard for subgradient methods. The theoretical guarantee for individual convergence of the regularized quasi-monotone … Read more

    Inexact Sequential Quadratic Optimization for Minimizing a Stochastic Objective Function Subject to Deterministic Nonlinear Equality Constraints

  • Frank E. Curtis
  • Daniel P. Robinson
  • Baoyu Zhou
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , , ,

    An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is assumed that constraint function and derivative values can be computed, but that only stochastic approximations are available for the objective function and its … Read more

    Polyhedral Analysis of a Polytope from a Service Center Location Problem with a Special Decision-Dependent Customer Demand

  • Fengqiao Luo
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Polyhedra Tags , , ,

    This paper establishes and analyzes a service center location model with a simple but novel decision-dependent demand induced from a maximum attraction principle. The model formulations are investigated in the distributionally-robust optimization framework for the capacitated and uncapacitated cases. A statistical model that is based on the maximum attraction principle for estimating customer demand and … Read more

    A framework for convex-constrained monotone nonlinear equations and its special cases

  • Max L. N. Gonçalves
  • Tiago Menezes
    • Categories Nonlinear Systems and Least-Squares

    This work refers to methods for solving convex-constrained monotone nonlinear equations. We first propose a framework, which is obtained by combining a safeguard strategy on the search directions with a notion of approximate projections. The global convergence of the framework is established under appropriate assumptions and some examples of methods which fall into this framework … Read more