Month: March 2012

Nonsmooth cone-constrained optimization with applications to semi-infinite programming

  • Boris S. Mordukhovich
  • Nghia Tran
    • Categories Nonsmooth Optimization, Semi-infinite Programming Tags , ,

    The paper is devoted to the study of general nonsmooth problems of cone-constrained optimization (or conic programming) important for various aspects of optimization theory and applications. Based on advanced constructions and techniques of variational analysis and generalized differentiation, we derive new necessary optimality conditions (in both “exact” and “fuzzy” forms) for nonsmooth conic programs, establish … Read more

    MILP formulation for islanding of power networks

  • Waqquas Bukhsh
  • Andreas Grothey
  • Kenneth McKinnon
  • Paul Trodden
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering

    In this paper, a mathematical formulation for the islanding of power networks is presented. Given an area of uncertainty in the network, the proposed approach uses mixed integer linear programming to isolate uncertain components and create islands, by intentionally (i) cutting lines, (ii) shedding loads and (iii) switching generators, while maximizing load supply. A key … Read more

    Stochastic Optimization Approach to Water Management in Cooling-Constrained Power Plants

  • Emil M. Constantinescu
  • Victor M. Zavala
  • Urmila Diwekar
  • Juan M. Salazar
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Stochastic Programming

    We propose a stochastic optimization framework to perform water management in coolingconstrained power plants. The approach determines optimal set-points to maximize power output in the presence of uncertain weather conditions and water intake constraints. Weather uncertainty is quantified in the form of ensembles using the state-of-the-art numerical weather prediction model WRF. The framework enables us … Read more

    A Low-Memory Approach For Best-State Estimation Of Hidden Markov Models With Model Error

  • Mihai Anitescu
  • Emil M. Constantinescu
  • Xiaoyan Zeng
    • Categories Civil and Environmental Engineering, Statistics, Unconstrained Optimization Tags , , , ,

    We present a low-memory approach for the best-state estimate (data assimilation) of hidden Markov models where model error is considered. In particular, our findings apply for the 4D- Var framework. The novelty of our approach resides in the fact that the storage needed by our estimation framework, while including model error, is dramatically reduced from … Read more

    A Dynamic Programming Heuristic for the Quadratic Knapsack Problem

  • Franklin Djeumou Fomeni
  • Adam N. Letchford
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Dynamic Programming Tags , ,

    It is well known that the standard (linear) knapsack problem can be solved exactly by dynamic programming in O(nc) time, where n is the number of items and c is the capacity of the knapsack. The quadratic knapsack problem, on the other hand, is NP-hard in the strong sense, which makes it unlikely that it … Read more

    Compact formulations of the Steiner traveling salesman problem and related problems

  • Adam N. Letchford
  • Saeideh Nasiri
  • Dirk Oliver Theis
    • Categories Combinatorial Optimization, Integer Programming Tags , ,

    The Steiner Traveling Salesman Problem (STSP) is a variant of the Traveling Salesman Problem (TSP) that is particularly suitable when dealing with sparse networks, such as road networks. The standard integer programming formulation of the STSP has an exponential number of constraints, just like the standard formulation of the TSP. On the other hand, there … Read more

    Level Bundle Methods for oracles with on-demand accuracy

  • Welington de Oliveira
  • Claudia Sagastizábal
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , , ,

    For nonsmooth convex optimization, we consider level bundle methods built using an oracle that computes values for the objective function and a subgradient at any given feasible point. For the problems of interest, the exact oracle information is computable, but difficult to obtain. In order to save computational effort the oracle can provide estimations with … Read more

    Logarithmic barriers for sparse matrix cones

  • Martin Andersen
  • Joachim Dahl
  • Lieven Vandenberghe
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , ,

    Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern, and its dual cone, the cone of sparse matrices with the same pattern that have a positive semidefinite completion. Efficient large-scale algorithms for evaluating these barriers … Read more

    On optimizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere

  • Zhang Lei-Hong
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Global Optimization Tags , , , ,

    Given symmetric matrices $B,D\in R^{n\times n}$ and a symmetric positive definite matrix $W\in R^{n\times n},$ maximizing the sum of the Rayleigh quotient $x^T Dx$ and the generalized Rayleigh quotient $x^T Bx/x^TWx$ on the unit sphere not only is of mathematical interest in its own right, but also finds applications in practice. In this paper, we … Read more

    Customizing the Solution Process of COIN-OR’s Linear Solvers with Python

  • Dominique Orban
  • Mehdi Towhidi
    • Categories (Mixed) Integer Linear Programming, Linear Programming, Optimization Software Design Principles Tags , , , , , ,

    Implementations of the Simplex method differ only in very specific aspects such as the pivot rule. Similarly, most relaxation methods for mixed-integer programming differ only in the type of cuts and the exploration of the search tree. Implementing instances of those frameworks would therefore be more efficient if linear and mixed-integer programming solvers let users … Read more