nonlinear programming

A primal-dual interior-point relaxation method with adaptively updating barrier for nonlinear programs

  • Yu-Hong Dai
  • Yakui Huang
  • Xin-Wei Liu
    • Categories Nonlinear Optimization Tags , , , ,

    Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel primal-dual interior-point relaxation method for nonlinear programs. In the proposed method, the barrier parameter is updated in every step as done in interior-point methods for linear programs, which is prominently different from the existing interior-point methods … Read more

    Mixed-Integer Optimal Control Problems with switching costs: A shortest path approach

  • Felix Bestehorn
  • Christoph Hansknecht
  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms Tags , , , ,

    We investigate an extension of Mixed-Integer Optimal Control Problems (MIOCPs) by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the … Read more

    A primal-dual modified log-barrier method for inequality constrained nonlinear optimization

  • Joshua D. Griffin
  • Riadh Omheni
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    We present a primal-dual modified log-barrier algorithm to solve inequality constrained nonlinear optimization problems. Basically, the algorithm is a Newton-like method applied to a perturbation of the optimality system that follows from a reformulation of the initial problem by introducing a modified log-barrier function to handle inequality constraints. The algorithm uses an outer/inner iteration scheme … Read more

    A Polynomial-time Algorithm with Tight Error Bounds for Single-period Unit Commitment Problem

  • S.C. Fang
  • Ruotian Gao
  • Wenxun Xing
  • Cheng Lu
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms, Scheduling Tags , , , ,

    This paper proposes a Lagrangian dual based polynomial-time approximation algorithm for solving the single-period unit commitment problem, which can be formulated as a mixed integer quadratic programming problem and proven to be NP-hard. Tight theoretical bounds for the absolute errors and relative errors of the approximate solutions generated by the proposed algorithm are provided. Computational … Read more

    Random projections for quadratic programs

  • Claudia D'Ambrosio
  • Leo Liberti
  • Pierre-Louis Poirion
  • Ky Vu
    • Categories Quadratic Programming Tags , , , ,

    Random projections map a set of points in a high dimensional space to a lower dimen- sional one while approximately preserving all pairwise Euclidean distances. While random projections are usually applied to numerical data, we show they can be successfully applied to quadratic programming formulations over a set of linear inequality constraints. Instead of solving … Read more

    Complexity and performance of an Augmented Lagrangian algorithm

  • Ernesto G. Birgin
  • José Mario Martínez
    • Categories Constrained Nonlinear Optimization Tags , , ,

    Algencan is a well established safeguarded Augmented Lagrangian algorithm introduced in [R. Andreani, E. G. Birgin, J. M. Martínez and M. L. Schuverdt, On Augmented Lagrangian methods with general lower-level constraints, SIAM Journal on Optimization 18, pp. 1286-1309, 2008]. Complexity results that report its worst-case behavior in terms of iterations and evaluations of functions and … Read more

    On the Complexity of an Augmented Lagrangian Method for Nonconvex Optimization

  • Geovani Nunes Grapiglia
  • Ya-xiang Yuan
    • Categories Nonlinear Optimization Tags , , ,

    In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity bound of $\mathcal{O}(|\log(\epsilon)|)$ outer iterations for the referred algorithm to generate an $\epsilon$-approximate KKT point, for $\epsilon\in (0,1)$. When the penalty parameters are unbounded, we prove … Read more

    A Shifted Primal-Dual Interior Method for Nonlinear Optimization

  • Philip E. Gill
  • Vyacheslav Kungurtsev
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization Tags , , , , , ,

    Interior methods provide an effective approach for the treatment of inequality constraints in nonlinearly constrained optimization. A new primal-dual interior method is proposed based on minimizing a sequence of shifted primal-dual penalty-barrier functions. Certain global convergence properties are established. In particular, it is shown that every limit point is either an infeasible stationary point, or … Read more

    Novel Radar Waveform Optimization for a Cooperative Radar-Communications System

  • Daniel W. Bliss
  • Hans D Mittelmann
  • Alex R. Chiriyath
  • Shankarachary Ragi
    • Categories Applications - Science and Engineering Tags , , , ,

    We develop and present the novel minimum estimation error variance waveform design method, that optimizes the spectral shape of a unimodular radar waveform such that the performance of a joint radar-communications system that shares spectrum is maximized. We also perform a numerical study to compare the performance of the new technique with the previously derived … Read more

    Large-scale packing of ellipsoids

  • Ernesto G. Birgin
  • R. D. Lobato
    • Categories Nonlinear Optimization Tags , , ,

    The problem of packing ellipsoids in the n-dimensional space is considered in the present work. The proposed approach combines heuristic techniques with the resolution of recently introduced nonlinear programming models in order to construct solutions with a large number of ellipsoids. Numerical experiments illustrate that the introduced approach delivers good quality solutions with a computational … Read more