trust-region methods

Intermediate Report on the development of an optimization code for smooth, high computing load, continuous objective functions when derivatives are not available

  • Frank Vanden Berghen
    • Categories Multidisciplinary Design Optimization, Unconstrained Optimization Tags ,

    We find very often in the industry simulators of huge chemical reactors, simulators of huge turbo-compressors, simulators of the path of a satellite in low orbit around earth, … These simulators were written to allow the design engineer to correctly estimate the consequences of the adjustment of one (or many) design variables (or parameters of … Read more

    On the Convergence of Successive Linear Programming Algorithms

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

    We analyze the global convergence properties of a class of penalty methods for nonlinear programming. These methods include successive linear programming approaches, and more specifically the SLP-EQP approach presented in \cite{ByrdGoulNoceWalt02}. Every iteration requires the solution of two trust region subproblems involving linear and quadratic models, respectively. The interaction between the trust regions of these … Read more

    A hybrid algorithm for nonlinear equality constrained optimization problems: global and local convergence theory

  • Mohammedi El Hallabi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Robust Optimization Tags , , , , , , ,

    In this paper we combine both trust-region and linesearch globalization strategies in a globally convergent hybrid algorithm to solve a continuously differentiable nonlinear equality constrained minimization problem. First, the trust-region approach is used to determine a descent direction of the augmented Lagrangian chosen as the merit function, and second, linesearch techniques are used to obtain … 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

    The Trust Region Subproblem and Semidefinite Programming

  • Charles Fortin
  • Henry Wolkowicz
    • Categories Convex Optimization, Semi-definite Programming, Unconstrained Optimization Tags , , ,

    The trust region subproblem (the minimization of a quadratic objective subject to one quadratic constraint and denoted TRS) has many applications in diverse areas, e.g. function minimization, sequential quadratic programming, regularization, ridge regression, and discrete optimization. In particular, it determines the step in trust region algorithms for function minimization. Trust region algorithms are popular for … Read more

    A Feasible Trust-Region Sequential Quadratic Programming Algorithm

  • M. J. Tenny
  • Stephen Wright
    • Categories Constrained Nonlinear Optimization Tags , ,

    An algorithm for smooth nonlinear constrained optimization problems is described, in which a sequence of feasible iterates is generated by solving a trust-region sequential quadratic programming (SQP) subproblem at each iteration, and perturbing the resulting step to retain feasibility of each iterate. By retaining feasibility, the algorithm avoids several complications of other trust-region SQP approaches: … Read more

    Space mapping: Models, sensitivities, and trust-regions methods

  • Luis Nunes Vicente
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , , ,

    The goal of this paper is to organize some of the mathematical and algorithmic aspects of the recently proposed space-mapping technique for continuous optimization with expensive function evaluations. First, we consider the mapping from the fine space to the coarse space when the models are vector-valued functions and when the space-mapping (nonlinear) least-squares residual is … Read more

    A New Trust Region Technique for the Maximum Weight Clique Problem

  • Stanislav Busygin
    • Categories Approximation Algorithms, Graphs and Matroids Tags , , , , , ,

    A new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a new trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of … Read more

    Lagrangean Duality Applied on Vehicle Routing with Time Windows

  • Brian Kallehauge
  • Jesper Larsen
  • Oli B.G. Madsen
    • Categories Cutting Plane Approaches, Nonsmooth Optimization, Transportation Tags , , , , ,

    This paper presents the results of the application of a non-differentiable optimization method in connection with the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW is an extension of the Vehicle Routing Problem. In the VRPTW the service at each customer must start within an associated time window. The Shortest Path decomposition of the … 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