Nonlinear Optimization

On regularized structure exploiting Quasi-Newton methods for ill-posed problems

  • Raphael Kuess
  • Andrea Walther
    • Categories Infinite Dimensional Optimization, Nonlinear Systems and Least-Squares Tags , , , ,

    Inverse problems are inherently ill-posed, leading standard optimization techniques to fail and necessitating the use of regularization. This paper introduces a regularized, structure-exploiting Powell-Symmetric-Broyden method under modified secant conditions for solving ill-posed inverse problems in both infinite dimensional and finite dimensional settings. Our approach integrates regularization and structure exploitation directly within the Quasi-Newton framework, leveraging … Read more

    Efficient search strategies for constrained multiobjective blackbox optimization

  • Sébastien Le Digabel
  • Antoine Lesage-Landry
  • Ludovic Salomon
  • Christophe Tribes
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags ,

    Multiobjective blackbox optimization deals with problems where the objective and constraint functions are the outputs of a numerical simulation. In this context, no derivatives are available, nor can they be approximated by finite differences, which precludes the use of classical gradient-based techniques. The DMulti-MADS algorithm implements a state-of-the-art direct search procedure for multiobjective blackbox optimization … Read more

    New Algorithms for maximizing the difference of convex functions

  • Aharon Ben-Tal
  • Luba Tetruashvili
    • Categories Global Optimization, Global Optimization Applications, Nonlinear Optimization

    Maximizing the difference of 2 convex functions over a convex feasible set (the so called DCA problem) is a hard problem. There is a large number of publications addressing this problem. Many of them are variations of widely used DCA algorithm [20]. The success of this algorithm to reach a good approximation of a global … Read more

    Optimistic Noise-Aware Sequential Quadratic Programming for Equality Constrained Optimization with Rank-Deficient Jacobians

  • Jiahao Shi
  • Baoyu Zhou
  • Albert S. Berahas
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

    We propose and analyze a sequential quadratic programming algorithm for minimizing a noisy nonlinear smooth function subject to noisy nonlinear smooth equality constraints. The algorithm uses a step decomposition strategy and, as a result, is robust to potential rank-deficiency in the constraints, allows for two different step size strategies, and has an early stopping mechanism. … Read more

    qpBAMM: a parallelizable ADMM approach for block-structured quadratic programs

  • Michel Lahmann
  • Christian Kirches
  • Martin T. Köhler
    • Categories Convex Optimization, Quadratic Programming Tags , , ,

    Block-structured quadratic programs (QPs) frequently arise in the context of the direct approach to solving optimal control problems. For successful application of direct optimal control algorithms to many real-world problems it is paramount that these QPs can be solved efficiently and reliably. Besides interior-point methods and active-set methods, ADMM-based quadratic programming approaches have gained popularity. … Read more

    NonOpt: Nonconvex, Nonsmooth Optimizer

  • Lara Zebiane
  • Frank E. Curtis
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , , ,

    NonOpt, a C++ software package for minimizing locally Lipschitz objective functions, is presented. The software is intended primarily for minimizing objective functions that are nonconvex and/or nonsmooth. The package has implementations of two main algorithmic strategies: a gradient-sampling and a proximal-bundle method. Each algorithmic strategy can employ quasi-Newton techniques for accelerating convergence in practice. The … Read more

    Sequential Rounding in Mixed-Integer Model Predictive Control

  • Artemi Makarow
  • Christian Kirches
    • Categories Approximation Algorithms, Control Applications, Systems governed by Differential Equations Optimization Tags , , ,

    This paper interfaces combinatorial integral approximation strategies with the inherent robustness properties of conventional model predictive control with stabilizing terminal conditions to establish practical asymptotic stability results for finite-control set and mixed-integer model predictive control. We examine the impact of sequential control rounding on the closed-loop performance in terms of stability and optimality. Sum-up rounding … Read more

    The Least Singular Value Function in Variational Analysis

  • Mario Jelitte
  • Boris S. Mordukhovich
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Nonsmooth Optimization Tags , , , ,

    Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, met- ric regularity can be elusive for some important ill-posed classes of problems includ- ing polynomial equations, parametric variational systems, smooth reformulations of complementarity systems with degenerate solutions, etc. The study of stability issues for such … Read more

    Optimal Control of Semilinear Graphon Systems

  • Martin T. Köhler
  • Artemi Makarow
  • Christian Kirches
    • Categories Infinite Dimensional Optimization, Network Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    Controlling the dynamics of large-scale networks is essential for a macroscopic reduction of overall consumption and losses in the context of energy supply, finance, logistics, and mobility. We investigate the optimal control of semilinear dynamical systems on asymptotically infinite networks, using the notion of graphons. Graphons represent a limit object of a converging graph sequence … Read more

    Obscured by terminology: Hidden parallels in direct methods for open-loop optimal control

  • Susanne Sass
  • Alexander Mitsos
    • Categories Control Applications, Scheduling, Systems governed by Differential Equations Optimization Tags , , , , ,

    Active research on optimal control methods comprises the developments of research groups from various fields, including control, mathematics, and process systems engineering. Although there is a consensus on the classification of the main solution methods, different terms are often used for the same method. For example, solving optimal control problems with control discretization and embedded … Read more