Nonlinear Optimization

New Variable Metric Methods for Unconstrained Minimization Covering the Large-Scale Case

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    A new family of numerically efficient variable metric or quasi-Newton methods for unconstrained minimization are given, which give simple possibility of adaptation for large-scale optimization. Global convergence of the methods can be established for convex sufficiently smooth functions. Some encouraging numerical experience is reported. CitationReport V876, Institute of Computer Science, AV CR, Pod Vodarenskou Vezi … Read more

    Interior-Point Method for Nonlinear Nonconvex Optimization

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags ,

    In this paper, we propose an algorithm for solving nonlinear nonconvex programming problems, which is based on the interior-point approach. Main theoretical results concern direction determination and step-length selection. We split inequality constraints into active and inactive to overcome problems with stability. Inactive constraints are eliminated directly while active constraints are used to define symmetric … Read more

    Nonsmooth Equation Method for Nonlinear Nonconvex Optimization

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags ,

    In this paper, we propose an algorithm for solving nonlinear nonconvex programming problems, which is based on the nonsmooth equation approach. This Algorithm was implemented in the interactive system for universal functional optimization UFO. Results of numerical experiments are reported. CitationReport V844, Institute of Computer Science, AV CR, Pod Vodarenskou Vezi 2, 18207 Praha 8, … Read more

    RIOTS_95–a MATLAB Toolbox for Solving General Optimal Control Problems And Its Applications to Chemical Processes

  • YangQuan Chen
  • Adam L. Schwartz
    • Categories Chemical Engineering, Problem Solving Environments, Systems governed by Differential Equations Optimization Tags , , , , ,

    RIOTS_95 is a group of programs and utilities, written mostly in C, Fortran and M-file scripts and designed as a toolbox for MATLAB, that provides an interactive environment for solving a very broad class of optimal control problems (OCP’s). RIOTS_95 comes pre-compiled for use with the Windows 95/98/2000 or Windows NT operating systems. The user’s … Read more

    Nonlinear Optimisation in CHP-Applications

  • Wilhelm Althaus
  • Michael Lucht
  • Michael Wigbels
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    At the Fraunhofer Institute UMSICHT a nonlinear model has been developed facilitating the dynamic optimisation of combined heat and power production systems. The strategy called “dynamic supply temperature optimisation” is a very promising approach to use the DH-network itself as a large heat storage causing no additional investment cost. The pipeline system of a district … Read more

    An Active-Set Algorithm for Nonlinear Programming Using Linear Programming and Equality Constrained Subproblems

  • Richard H. Byrd
  • Nicholas I. M. Gould
  • Jorge Nocedal
  • Richard A. Waltz
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark Tags , , , , ,

    This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained … Read more

    A Primal-Dual Trust Region Algorithm for Nonlinear Optimization

  • Michael Gertz
  • Philip E. Gill
    • Categories Constrained Nonlinear Optimization Tags

    This paper concerns general (nonconvex) nonlinear optimization when first and second derivatives of the objective and constraint functions are available. The proposed method is based on finding an approximate solution of a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penalty-barrier function that involves … Read more

    A Simple Primal-Dual Feasible Interior-Point Methodfor Nonlinear Programming with Monotone Descent

  • Sasan Bakhtiari
  • André L. Tits
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    We propose and analyze a primal-dual interior point method of the “feasible” type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is the use of different barrier parameter values for each constraint, with the purpose of better steering the constructed sequence away from non-KKT stationary … Read more

    On the superlinear local convergence of a filter-SQP method

  • Stefan Ulbrich
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    Transition to superlinear local convergence is shown for a modified version of the trust-region filter-SQP method for nonlinear programming introduced by Fletcher, Leyffer, and Toint [8]. Hereby, the original trust-region SQP-steps can be used without an additional second order correction. The main modification consists in using the Lagrangian function value instead of the objective function … Read more

    Semidefinite optimization, a spectral approach

  • M.A. van Bossum
    • Categories Nonlinear Optimization, Semi-definite Programming Tags , , , , , , ,

    This thesis is about mathematical optimization. Mathematical optimization involves the construction of methods to solve optimization problems, which can arise from real-life problems in applied science, when they are mathematically modeled. Examples come from electrical design, engineering, control theory, telecommunication, environment, finance, and logistics. This thesis deals especially with semidefinite optimization problems. Semidefinite programming is … Read more