exact penalty functions

Improved Penalty Algorithm for Mixed Integer PDE Constrained Optimization (MIPDECO) Problems

  • Dominik Garmatter
  • Margherita Porcelli
  • Francesco Rinaldi
  • Martin Stoll
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Optimization of Systems modeled by PDEs Tags , , ,

    Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized PDEs. So far, the Branch-and-Bound framework has been the most common solution strategy for such problems. In order to provide an alternative solution approach, especially … Read more

    An Inexact First-order Method for Constrained Nonlinear Optimization

  • Yuyang Rong
  • Jiashan Wang
  • Hao Wang
  • Hudie Zhou
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , ,

    The primary focus of this paper is on designing inexact first-order methods for solving large-scale constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the computational cost needed for each iteration. A penalty parameter updating strategy during the subproblem solve enables the algorithm to automatically detect infeasibility. Global … Read more

    A Dynamic Penalty Parameter Updating Strategy for Matrix-Free Sequential Quadratic Optimization

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

    This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation of the search direction during each iteration, for which we consider the use of matrix-free methods. In particular, we develop a method … Read more

    Error bounds for rank constrained optimization problems and applications

  • Shaohua Pan
  • Shujun Shujun
    • Categories Applications - OR and Management Sciences Tags , , ,

    This paper is concerned with the rank constrained optimization problem whose feasible set is the intersection of the rank constraint set $\mathcal{R}=\!\big\{X\in\mathbb{X}\ |\ {\rm rank}(X)\le \kappa\big\}$ and a closed convex set $\Omega$. We establish the local (global) Lipschitzian type error bounds for estimating the distance from any $X\in \Omega$ ($X\in\mathbb{X}$) to the feasible set and … Read more

    Exact penalty decomposition method for zero-norm minimization based on MPEC formulation

  • Xiaolan Liu
  • Shaohua Pan
  • Shujun Shujun
    • Categories Applications - OR and Management Sciences Tags , , ,

    We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Then, by the special structure of the exact penalty problem, we propose a decomposition method that can seek a global optimal solution of the … Read more

    A DERIVATIVE-FREE APPROACH TO CONSTRAINED MULTIOBJECTIVE NONSMOOTH OPTIMIZATION

  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. We define a linesearch-based solution method, and we show that it converges to a set of Pareto stationary points. To this … Read more

    Iterative Reweighted Linear Least Squares for Exact Penalty Subproblems on Product Sets

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

    We present two matrix-free methods for solving exact penalty subproblems on product sets that arise when solving large-scale optimization problems. The first approach is a novel iterative reweighting algorithm (IRWA), which iteratively minimizes quadratic models of relaxed subproblems while automatically updating a relaxation vector. The second approach is based on alternating direction augmented Lagrangian (ADAL) … Read more

    A Linesearch-based Derivative-free Approach for Nonsmooth Optimization

  • Giovanni Fasano
  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    In this paper, we propose new linesearch-based methods for nonsmooth optimization problems when first-order information on the problem functions is not available. In the first part, we describe a general framework for bound-constrained problems and analyze its convergence towards stationary points, using the Clarke-Jahn directional derivative. In the second part, we consider inequality constrained optimization … Read more

    Constraint Reduction with Exact Penalization for Model-Predictive Rotorcraft Control

  • Aaron L. Greenfield
  • Meiyun Y. He
  • Vineet Sahasrabudhe
  • AndrĂ© L. Tits
    • Categories Applications - Science and Engineering, Control Applications, Quadratic Programming Tags , , , , , , , , ,

    Model Predictive Control (also known as Receding Horizon Control (RHC)) has been highly successful in process control applications. Its use for aerospace applications has been hindered by its high computational requirements. In the present paper, we propose using enhanced primal-dual interior-point optimization techniques in the convex-quadratic-program-based RHC control of a rotorcraft. Our enhancements include a … Read more

    Differentiable exact penalty functions for nonlinear second-order cone programs

  • Ellen H. Fukuda
  • Paulo J. S. Silva
  • Masao Fukushima
    • Categories Nonlinear Optimization, Second-Order Cone Programming Tags , , ,

    We propose a method to solve nonlinear second-order cone programs (SOCPs), based on a continuously differentiable exact penalty function. The construction of the penalty function is given by incorporating a multipliers estimate in the augmented Lagrangian for SOCPs. Under the nondegeneracy assumption and the strong second-order sufficient condition, we show that a generalized Newton method … Read more