Nonlinear Optimization

Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization

  • Saeed Ghadimi
  • Guanghui Lan
  • Hongchao Zhang
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization Tags , , , , , ,

    This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but convex) component. In order to solve these problems, we propose a randomized stochastic projected gradient (RSPG) algorithm, in which proper mini-batch of samples are … Read more

    A Sequential Quadratic Optimization Algorithm with Rapid Infeasibility Detection

  • James V. Burke
  • Frank E. Curtis
  • Hao Wang
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    We present a sequential quadratic optimization (SQO) algorithm for nonlinear constrained optimization. The method attains all of the strong global and fast local convergence guarantees of classical SQO methods, but has the important additional feature that fast local convergence is guaranteed when the algorithm is employed to solve infeasible instances. A two-phase strategy, carefully constructed … Read more

    Cooperative Wireless Sensor Network Positioning via Implicit Convex Feasibility

  • Yair Censor
  • Mohammad R. Gholami
  • Erik G. Strom
  • Luba Tetruashvili
    • Categories Facility Planning and Design, Nonlinear Optimization Tags , , , ,

    We propose a distributed positioning algorithm to estimate the unknown positions of a number of target nodes, given distance measurements between target nodes and between target nodes and a number of reference nodes at known positions. Based on a geometric interpretation, we formulate the positioning problem as an implicit convex feasibility problem in which some … Read more

    Some Remarks for a Decomposition of Linear-Quadratic Optimal Control Problems for Two-Steps Systems

  • Shahlar Meherrem
    • Categories Nonlinear Optimization Tags ,

    In this paper we obtained new approach for the problem, which it is described in reference[1,2]. In the references [1], the authors are studied Decomposition of Linear-Quadratic optimal Control problems for Two-Steps Systems. In [1], the authors assumed the switching point is fixed and it is given algorithm for solving Linear-Quadratic optimal Control problem. But … Read more

    Local Convergence of the Method of Multipliers for Variational and Optimization Problems under the Sole Noncriticality Assumption

  • Alexey F. Izmailov
  • A. S. Kurennoy
  • Mikhail V. Solodov
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , , ,

    We present local convergence analysis of the method of multipliers for equality-constrained variational problems (in the special case of optimization, also called the augmented Lagrangian method) under the sole assumption that the dual starting point is close to a noncritical Lagrange multiplier (which is weaker than second-order sufficiency). Local superlinear convergence is established under the … Read more

    Projected subgradient minimization versus superiorization

  • Yair Censor
  • Ran Davidi
  • Gabor T. Herman
  • Reinhard W. Schulte
  • Luba Tetruashvili
    • Categories Biomedical Applications, Constrained Nonlinear Optimization Tags , , , , , , , ,

    The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to regain feasibility. The latter poses a computational difficulty and, therefore, the projected subgradient method is applicable only when the feasible region is “simple … Read more

    Convergence Analysis of DC Algorithm for DC programming with subanalytic data

  • Hoai An Le Thi
  • Huynh Van Ngai
  • Tao Pham Dinh
    • Categories Nonlinear Optimization, Transportation Tags , , , ,

    DC Programming and DCA have been introduced by Pham Dinh Tao in 1986 and extensively developed by Le Thi Hoai An and Pham Dinh Tao since 1993. These approaches have been successfully applied to solving real life problems in their large scale setting. In this paper, by using the Lojasiewicz inequality for nonsmooth subanalytic functions, … Read more

    Optimization of running strategies based on anaerobic energy and variations of velocity

  • Amandine Aftalion
  • Joseph Frédéric Bonnans
    • Categories Biomedical Applications, Systems governed by Differential Equations Optimization Tags , , , , , ,

    We present new models, numerical simulations and rigorous analysis for the optimization of the velocity in a race. In a seminal paper, Keller (1973,1974) explained how a runner should determine his speed in order to run a given distance in the shortest time. We extend this analysis, based on the equation of motion and aerobic … Read more

    Algebraic rules for quadratic regularization of Newton’s method

  • Elizabeth Wegner Karas
  • Sandra Augusta Santos
  • Benar Fux Svaiter
    • Categories Unconstrained Optimization Tags , , , ,

    In this work we propose a class of quasi-Newton methods to minimize a twice differentiable function with Lipschitz continuous Hessian. These methods are based on the quadratic regularization of Newton’s method, with algebraic explicit rules for computing the regularizing parameter. The convergence properties of this class of methods are analysed. We show that if the … Read more

    A New Framework for Combining Global and Local Methods in Black Box Optimization

  • Yibo Ji
  • Sujin Kim
  • Wendy Lu Xu
    • Categories Applications - OR and Management Sciences, Bound-constrained Optimization, Global Optimization

    We propose a new framework for the optimization of computationally expensive black box problems, where neither closed-form expressions nor derivatives of the objective functions are available. The proposed framework consists of two procedures. The first constructs a global metamodel to approximate the underlying black box function and explores an unvisited area to search for a … Read more