Holder Metric Subregularity with Applications to Proximal Point Method

  • Guoyin Li
  • Boris S. Mordukhovich
    • Categories Nonsmooth Optimization Tags , , , ,

    This paper is mainly devoted to the study and applications of H\”older metric subregularity (or metric $q$-subregularity of order $q\in(0,1]$) for general set-valued mappings between infinite-dimensional spaces. Employing advanced techniques of variational analysis and generalized differentiation, we derive neighborhood and pointbased sufficient conditions as well as necessary conditions for $q$-metric subregularity with evaluating the exact … Read more

    Bundle method for non-convex minimization with inexact subgradients and function values

  • Dominikus Noll
    • Categories Control Applications, Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , ,

    We discuss a bundle method to minimize non-smooth and non-convex locally Lipschitz functions. We analyze situations where only inexact subgradients or function values are available. For suitable classes of non-smooth functions we prove convergence of our algorithm to approximate critical points. CitationTo appear in: Computational and Analytical Mathematics. Springer Proceedings in MathematicsArticleDownload View PDF

    Large Neighborhood Search for LNG Inventory Routing

  • Amr El-bakry
  • Kevin C Furman
  • Vikas Goel
  • Jin-hwa Song
    • Categories Transportation

    Liquefied Natural Gas (LNG) is steadily becoming a common mode for commercializing natural gas. Due to the capital intensive nature of LNG projects, the optimal design of LNG supply chains is extremely important from a profitability perspective. Motivated by the need for a model that can assist in the design analysis of LNG supply chains, … Read more

    Exact and heuristic approaches to the budget-constrained dynamic uncapacitated facility location-network design problem

  • Natashia Boland
  • Abdolsalam Ghaderi
  • Mohammad Saeid JabalAmeli
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design, Meta Heuristics Tags , , , ,

    Facility location-network design problems seek to simultaneously determine the locations of fa- cilities and the design of the network connecting the facilities so as to best serve a set of clients accessing the facilities via the network. Here we study a dynamic (multi-period) version of the problem, subject to a budget constraint limiting the investment … Read more

    Constraint Reduction with Exact Penalization for Model-Predictive Rotorcraft Control

  • Aaron L. Greenfield
  • Meiyun Y. He
  • Vineet Sahasrabudhe
  • AndrĂ© L. Tits
    • Categories Applications - Science and Engineering, Control Applications, Quadratic Programming Tags , , , , , , , , ,

    Model Predictive Control (also known as Receding Horizon Control (RHC)) has been highly successful in process control applications. Its use for aerospace applications has been hindered by its high computational requirements. In the present paper, we propose using enhanced primal-dual interior-point optimization techniques in the convex-quadratic-program-based RHC control of a rotorcraft. Our enhancements include a … Read more

    Reformulation of a model for hierarchical divisive graph modularity maximization

  • Sonia Cafieri
  • Alberto Costa
  • Pierre Hansen
    • Categories Convex Optimization, Network Optimization, Quadratic Programming Tags , , ,

    Finding clusters, or communities, in a graph, or network is a very important problem which arises in many domains. Several models were proposed for its solution. One of the most studied and exploited is the maximization of the so called modularity, which represents the sum over all communities of the fraction of edges within these … Read more

    A PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS

  • Tran Van Hao
  • Nguyen Huu Thong
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Stochastic Approaches Tags , , ,

    This paper proposes a new probabilistic algorithm for solving multi-objective optimization problems – Probability-Driven Search Algorithm. The algorithm uses probabilities to control the process in search of Pareto optimal solutions. Especially, we use the absorbing Markov Chain to argue the convergence of the algorithm. We test this approach by implementing the algorithm on some benchmark … Read more

    Subgradient methods for huge-scale optimization problems

  • Yurii Nesterov
    • Categories Nonsmooth Optimization Tags , , , ,

    We consider a new class of huge-scale problems, the problems with {\em sparse subgradients}. The most important functions of this type are piece-wise linear. For optimization problems with uniform sparsity of corresponding linear operators, we suggest a very efficient implementation of subgradient iterations, which total cost depends {\em logarithmically} in the dimension. This technique is … Read more

    Globally Convergent Evolution Strategies and CMA-ES

  • Youssef Diouane
  • Serge Gratton
  • Luis Nunes Vicente
    • Categories Unconstrained Optimization Tags , , ,

    In this paper we show how to modify a large class of evolution strategies (ES) to rigorously achieve a form of global convergence, meaning convergence to stationary points independently of the starting point. The type of ES under consideration recombine the parents by means of a weighted sum, around which the offsprings are computed by … Read more

    Smoothing and Worst Case Complexity for Direct-Search Methods in Non-Smooth Optimization

  • R. Garmanjani
  • Luis Nunes Vicente
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , , , , ,

    For smooth objective functions it has been shown that the worst case cost of direct-search methods is of the same order as the one of steepest descent, when measured in number of iterations to achieve a certain threshold of stationarity. Motivated by the lack of such a result in the non-smooth case, we propose, analyze, … Read more