Path Constraints in Tychastic and Unscented Optimal Control: Theory, Applications and Experimental Results

  • M. Karpenko
  • Isaac Ross
  • R. J. Proulx
    • Categories Applications - Science and Engineering, Robust Optimization, Stochastic Programming Tags , ,

    In recent papers, we have shown that a Lebesgue-Stieltjes optimal control theory forms the foundations for unscented optimal control. In this paper, we further our results by incorporating uncertain mixed state-control constraints in the problem formulation. We show that the integrated Hamiltonian minimization condition resembles a semi-infinite type mathematical programming problem. The resulting computational difficulties … Read more

    The Sound of APALM Clapping: Faster Nonsmooth Nonconvex Optimization with Stochastic Asynchronous PALM

  • Damek Davis
  • Brent Edmunds
  • Madeleine Udell
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    We introduce the Stochastic Asynchronous Proximal Alternating Linearized Minimization (SAPALM) method, a block coordinate stochastic proximal-gradient method for solving nonconvex, nonsmooth optimization problems. SAPALM is the first asynchronous parallel optimization method that provably converges on a large class of nonconvex, nonsmooth problems. We prove that SAPALM matches the best known rates of convergence — among … Read more

    Mixed-integer Programming Based Approaches for the Movement Planner Problem: Model, Heuristics and Decomposition

  • Chiwei Yan
  • Luyi Yang
    • Categories Scheduling, Transportation Tags , , , ,

    This is the first prize winning report for the 2012 INFORMS Railway Application Section Problem Solving Competition (https://www.informs.org/Community/RAS/Problem-Solving-Competition/2012-RAS-Problem-Solving-Competition). ArticleDownload View PDF

    Some cut-generating functions for second-order conic sets

  • Santanu S. Dey
  • Asteroide Santana
    • Categories Cutting Plane Approaches, Integer Programming

    In this paper, we study cut generating functions for conic sets. Our first main result shows that if the conic set is bounded, then cut generating functions for integer linear programs can easily be adapted to give the integer hull of the conic integer program. Then we introduce a new class of cut generating functions … Read more

    Complexity of Routing Problems with Release Dates and Deadlines

  • Alan L. Erera
  • Damian Reyes
  • Martin Savelsbergh
    • Categories Combinatorial Optimization, Transportation Tags , ,

    The desire of companies to offer same-day delivery leads to interesting new routing problems. We study the complexity of a setting in which a delivery to a customer is guaranteed to take place within a pre-specified time after the customer places the order. Thus, an order has a release date (when the order is placed) … Read more

    Effects of Uncertain Requirements on the Architecture Selection Problem

  • Somayeh Moazeni
  • Roshanak Nilchiani
    • Categories Applications - Science and Engineering, Multidisciplinary Design Optimization, Robust Optimization Tags , , ,

    The problem of identifying a specific design or architecture that allows to satisfy all the system requirements becomes more difficult when uncertainties are taken into account. When a requirement is subject to uncertainty there are a number approaches available to the system engineer, each one with its own benefits and disadvantages. Classical robust optimization is … Read more

    Efficient Symmetric Hessian Propagation for Direct Optimal Control

  • Moritz Diehl
  • Boris Houska
  • Rien Quirynen
    • Categories Systems governed by Differential Equations Optimization Tags , , ,

    Direct optimal control algorithms first discretize the continuous-time optimal control problem and then solve the resulting finite dimensional optimization problem. If Newton type optimization algorithms are used for solving the discretized problem, accurate first as well as second order sensitivity information needs to be computed. This article develops a novel approach for computing Hessian matrices … Read more

    Lifted Collocation Integrators for Direct Optimal Control in ACADO Toolkit

  • Moritz Diehl
  • Sebastien Gros
  • Boris Houska
  • Rien Quirynen
    • Categories Systems governed by Differential Equations Optimization Tags , , ,

    This paper presents a class of efficient Newton-type algorithms for solving the nonlinear programs (NLPs) arising from applying a direct collocation approach to continuous time optimal control. The idea is based on an implicit lifting technique including a condensing and expansion step, such that the structure of each subproblem corresponds to that of the multiple … Read more

    SCORE Allocations for Bi-objective Ranking and Selection

  • Guy Feldman
  • Susan R. Hunter
    • Categories Global Optimization, Multi-Criteria Optimization, Stochastic Programming Tags , ,

    The bi-objective R&S problem is a special case of the multi-objective simulation optimization problem in which two conflicting objectives are known only through dependent Monte Carlo estimators, the decision space or number of systems is finite, and each system can be sampled to some extent. The solution to the bi-objective R&S problem is a set … Read more

    Ellipsoidal Mixed-Integer Representability

  • Alberto Del Pia
  • Jeffrey Poskin
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory

    Representability results for mixed-integer linear systems play a fundamental role in optimization since they give geometric characterizations of the feasible sets that can be formulated by mixed-integer linear programming. We consider a natural extension of mixed-integer linear systems obtained by adding just one ellipsoidal inequality. The set of points that can be described, possibly using … Read more