Constrained Nonlinear Optimization

Performance of CONDOR, a Parallel, Constrained extension of Powell’s UOBYQA algorithm. Experimental results and comparison with the DFO algorithm.

  • Hugues Bersini
  • Frank Vanden Berghen
    • Categories Constrained Nonlinear Optimization, Optimization of Systems modeled by PDEs, Parallel Algorithms Tags , , ,

    This paper presents an algorithmic extension of Powell’s UOBYQA algorithm (”Unconstrained Optimization BY Quadratical Approximation”). We start by summarizing the original algorithm of Powell and by presenting it in a more comprehensible form. Thereafter, we report comparative numerical results between UOBYQA, DFO and a parallel, constrained extension of UOBYQA that will be called in the … Read more

    Convergence Analysis of the DIRECT Algorithm

  • D. E. Finkel
  • C. T. Kelley
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Nonsmooth Optimization Tags , , ,

    The DIRECT algorithm is a deterministic sampling method for bound constrained Lipschitz continuous optimization. We prove a subsequential convergence result for the DIRECT algorithm that quantifies some of the convergence observations in the literature. Our results apply to several variations on the original method, including one that will handle general constraints. We use techniques from … Read more

    GLOBAL CONVERGENCE OF AN ELASTIC MODE APPROACH FOR A CLASS OF MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

  • Mihai Anitescu
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Mechanical Engineering Tags , , ,

    We prove that any accumulation point of an elastic mode approach, applied to the optimization of a mixed P variational inequality, that approximately solves the relaxed subproblems is a C-stationary point of the problem of optimizing a parametric mixed P variational inequality. If, in addition, the accumulation point satis es the MPCC-LICQ constraint quali cation and if … Read more

    ON USING THE ELASTIC MODE IN NONLINEAR PROGRAMMING APPROACHES TO MATHEMATICALPROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

  • Mihai Anitescu
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , ,

    We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using algorithms and procedures of smooth nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sucient conditions for their Lagrange multiplier set to be nonempty. MPCCs that have nonempty Lagrange multiplier sets and that satisfy the quadratic growth condition can … Read more

    Convergence analysis of a primal-dual interior-point method for nonlinear programming

  • Igor Griva
  • David F. Shanno
  • Robert J. Vanderbei
    • Categories Constrained Nonlinear Optimization Tags , ,

    We analyze a primal-dual interior-point method for nonlinear programming. We prove the global convergence for a wide class of problems under the standard assumptions on the problem. CitationTechnical Report ORFE-04-07, Department of ORFE, Princeton University, Princeton, NJ 08544ArticleDownload View PDF

    A primal-dual nonlinear rescaling method with dynamic scaling parameter update

  • Igor Griva
  • Roman Polyak
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    In this paper we developed a general primal-dual nonlinear rescaling method with dynamic scaling parameter update (PDNRD) for convex optimization. We proved the global convergence, established 1.5-Q-superlinear rate of convergence under the standard second order optimality conditions. The PDNRD was numerically implemented and tested on a number of nonlinear problems from COPS and CUTE sets. … Read more

    Numerical experiments with an interior-exterior point method for nonlinear programming

  • Igor Griva
    • Categories Constrained Nonlinear Optimization Tags , , ,

    The paper presents an algorithm for solving nonlinear programming problems. The algorithm is based on the combination of interior and exterior point methods. The latter is also known as the primal-dual nonlinear rescaling method. The paper shows that in certain cases when the interior point method fails to achieve the solution with the high level … Read more

    Constrained optimization in seismic reflection tomography: an SQP augmented Lagrangian approach

  • Frederic Delbos
  • Jean Charles Gilbert
  • R. Glowinski
  • D. Sinoquet
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Quadratic Programming Tags , , , , , ,

    Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint, the problem consists in minimizing a nonlinear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori … Read more

    A sequential quadratic programming algorithm with a piecewise linear merit function

  • Francisco Gomes
    • Categories Constrained Nonlinear Optimization Tags , ,

    A sequential quadratic programming algorithm for solving nonlinear programming problems is presented. The new feature of the algorithm is related to the definition of the merit function. Instead of using one penalty parameter per iteration and increasing it as the algorithm progresses, we suggest that a new point is to be accepted if it stays … Read more

    Benchmarking Optimization Software with COPS 3.0

  • Elizabeth D. Dolan
  • Jorge MorĂ©
  • Todd S. Munson
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark

    We describe version 3.0 of the COPS set of nonlinearly constrained optimization problems. We have added new problems, as well as streamlined and improved most of the problems. We also provide a comparison of the FILTER, KNITRO, LOQO, MINOS, and SNOPT solvers on these problems. CitationTechnical Report ANL/MCS-TM-273, Argonne National Laboratory, 02/04.ArticleDownload View PDF