large-scale optimization

Interior-Point Methods for Nonconvex Nonlinear Programming: Complementarity Constraints

  • Hande Benson
  • David F. Shanno
  • Robert J. Vanderbei
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , ,

    In this paper, we present the formulation and solution of optimization problems with complementarity constraints using an interior-point method for nonconvex nonlinear programming. We identify possible difficulties that could arise, such as unbounded faces of dual variables, linear dependence of constraint gradients and initialization issues. We suggest remedies. We include encouraging numerical results on the … Read more

    A Comparative Study of Large-Scale Nonlinear Optimization Algorithms

  • Hande Benson
  • David F. Shanno
  • Robert J. Vanderbei
    • Categories Constrained Nonlinear Optimization, Quadratic Programming, Unconstrained Optimization Tags , ,

    In recent years, much work has been done on implementing a variety of algorithms in nonlinear programming software. In this paper, we analyze the performance of several state-of-the-art optimization codes on large-scale nonlinear optimization problems. Extensive numerical results are presented on different classes of problems, and features of each code that make it efficient or … Read more

    Automatic Differentiation Tools in Optimization Software

  • Jorge Moré
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems Tags , , ,

    We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our discussion centers on the computation of the gradient and Hessian matrix for partially separable functions and shows that the … Read more

    Extra-Updates Criterion for the Limited Memory BFGS Algorithm for Large Scale Nonlinear Optimization

  • Mehiddin Al-Baali
    • Categories Unconstrained Optimization Tags , ,

    This paper studies recent modifications of the limited memory BFGS (L-BFGS) method for solving large scale unconstrained optimization problems. Each modification technique attempts to improve the quality of the L-BFGS Hessian by employing (extra) updates in certain sense. Because at some iterations these updates might be redundant or worsen the quality of this Hessian, this … Read more

    Feasible Interior Methods Using Slacks for Nonlinear Optimization

  • Richard H. Byrd
  • Richard A. Waltz
  • Jorge Nocedal
    • Categories Constrained Nonlinear Optimization Tags , , , , , , , ,

    A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the … Read more

    GPCG: A case study in the performance and scalability of optimization algorithms

  • Steven Benson
  • Lois McInnes
  • Jorge Moré
    • Categories Optimization Software Design Principles, Parallel Algorithms, Problem Solving Environments Tags , ,

    GPCG is an algorithm within the Toolkit for Advanced Optimization (TAO) for solving bound constrained, convex quadratic problems. Originally developed by More’ and Toraldo, this algorithm was designed for large-scale problems but had been implemented only for a single processor. The TAO implementation is available for a wide range of high-performance architecture, and has been … Read more

    Benchmarking Optimization Software with COPS

  • Elizabeth D. Dolan
  • Jorge Moré
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark Tags ,

    We describe version 2.0 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 LANCELOT, LOQO, MINOS, and SNOPT solvers on these problems. CitationTechnical Report ANL/MCS-246 Mathematics and Computer Science Division Argonne National Laboratory … Read more