Data Fitting and Experimental Design in Dynamical Systems with EASY-FIT ModelDesign

  • Klaus Schittkowski
    • Categories Nonlinear Systems and Least-Squares, Problem Solving Environments, Systems governed by Differential Equations Optimization

    EASY-FIT is an interactive software system to identify parameters and compute optimal designs in explicit model functions, steady-state systems, Laplace transformations, systems of ordinary differential equations, differential algebraic equations, or systems of one-dimensional time dependent partial differential equations with or without algebraic equations. Proceeding from given experimental data, i.e. observation times and measurements, the minimum … Read more

    A new sequential optimality condition for constrained optimization and algorithmic consequences

  • Roberto Andreani
  • José Mario Martínez
  • Benar Fux Svaiter
    • Categories Nonlinear Optimization Tags , , ,

    Necessary first-order sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. These conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qual- i cations. A new strong sequential optimality condition is introduced in the present paper. A proof that a well established Augmented Lagrangian … Read more

    Local superlinear convergence of polynomial-time interior-point methods for hyperbolic cone optimization problems

  • Yurii Nesterov
  • Levent Tunçel
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    In this paper, we establish the local superlinear convergence property of some polynomial-time interior-point methods for an important family of conic optimization problems. The main structural property used in our analysis is the logarithmic homogeneity of self-concordant barrier function, which must have {\em negative curvature}. We propose a new path-following predictor-corrector scheme, which work only … Read more

    An L1 Elastic Interior-Point Method for Mathematical Programs with Complementarity Constraints

  • Zoumana Coulibaly
  • Dominique Orban
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , , , ,

    We propose an interior-point algorithm based on an elastic formulation of the L1-penalty merit function for mathematical programs with complementarity constraints. The method generalizes that of Gould, Orban and Toint (2003) and naturally converges to a strongly stationary point or delivers a certificate of degeneracy without recourse to second-order intermediate solutions. Remarkably, the method allows … Read more

    A Factorization with Update Procedures for a KKT Matrix Arising in Direct Optimal Control

  • Hans Georg Bock
  • Christian Kirches
  • Sebastian Sager
  • Johannes P. Schlöder
    • Categories Quadratic Programming, Systems governed by Differential Equations Optimization Tags , ,

    Quadratic programs obtained for optimal control problems of dynamic or discrete–time processes usually involve highly block structured Hessian and constraints matrices. Efficient numerical methods for the solution of such QPs have to respect and exploit this block structure. In interior point methods, this is elegantly achieved by the widespread availability of advanced sparse symmetric indefinite … Read more

    An Improved Branch-and-Bound Method for Maximum Monomial Agreement

  • Jonathan Eckstein
  • Noam Goldberg
    • Categories 0-1 Programming, Branch and Cut Algorithms, Data-Mining Tags , , , ,

    The NP-hard Maximum Monomial Agreement (MMA) problem consists of finding a single logical conjunction that best fits a weighted dataset of “positive” and “negative” binary vectors. Computing classifiers using boosting methods involves a maximum agreement subproblem at each iteration, although such subproblems are typically solved by heuristic methods. Here, we describe an exact branch and … Read more

    Tightened L0 Relaxation Penalties for Classification

  • Jonathan Eckstein
  • Noam Goldberg
    • Categories (Mixed) Integer Linear Programming, Data-Mining, Statistics Tags , , , , , ,

    In optimization-based classification model selection, for example when using linear programming formulations, a standard approach is to penalize the L1 norm of some linear functional in order to select sparse models. Instead, we propose a novel integer linear program for sparse classifier selection, generalizing the minimum disagreement hyperplane problem whose complexity has been investigated in … Read more

    Most tensor problems are NP-hard

  • Christopher Hillar
  • Lek-Heng Lim
    • Categories Applications - Science and Engineering, Global Optimization Theory, Graphs and Matroids Tags , , , , , , , , , ,

    We show that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list here includes: determining the feasibility of a system of bilinear equations, deciding whether a tensor possesses a given eigenvalue, singular value, or spectral norm; approximating an eigenvalue, eigenvector, singular vector, or spectral norm; determining a best … Read more

    A Time Bucket Formulation for the TSP with Time Windows

  • Sanjeeb Dash
  • Oktay Gunluk
  • Andrea Lodi
  • Andrea Tramontani
    • Categories Integer Programming

    The Traveling Salesman Problem with Time Windows (TSPTW) is the problem of finding a minimum-cost path visiting a set of cities exactly once, where each city must be visited within a given time window. We present an extended formulation for the problem based on partitioning the time windows into sub-windows, which we call “buckets”. We … Read more

    A Facial Reduction Algorithm for Finding Sparse SOS Representations

  • Masakazu Muramatsu
  • Hayato Waki
    • Categories Convex Optimization, Global Optimization Theory, Semi-definite Programming Tags , , ,

    Facial reduction algorithm reduces the size of the positive semidefinite cone in SDP. The elimination method for a sparse SOS polynomial ([3]) removes unnecessary monomials for an SOS representation. In this paper, we establish a relationship between a facial reduction algorithm and the elimination method for a sparse SOS polynomial. CitationTechnical Report CS-09-02, Department of … Read more