Applications – Science and Engineering

Majorization-minimization procedures and convergence of SQP methods for semi-algebraic and tame programs

  • Jérôme Bolte
  • Edouard Pauwels
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , , , , , , ,

    In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques from semi-algebraic geometry and variational analysis –in particular Lojasiewicz inequality– we establish the convergence of sequences generated by this type of schemes to critical points. The … Read more

    The Descriptor Continuous-Time Algebraic Riccati Equation. Numerical Solutions and Some Direct Applications

  • Claudiu Dinicu
    • Categories Applications - Science and Engineering, Robust Optimization Tags , , ,

    We investigate here the numerical solution of a special type of descriptor continuous-time Riccati equation which is involved in solving several key problems in robust control, formulated under very general hypotheses. We also give necessary and sufficient existence conditions together with computable formulas for both stabilizing and antistabilizing solutions in terms of the associated matrix … Read more

    Convergence Analysis of Primal-Dual Based Methods for Total Variation Minimization with Finite Element Approximation

  • Wenyi Tian
  • Xiao-Ming Yuan
    • Categories Applications - Science and Engineering Tags , , , ,

    We consider the total variation minimization model with consistent finite element discretization. It has been shown in the literature that this model can be reformulated as a saddle-point problem and be efficiently solved by the primal-dual method. The convergence for this application of the primal-dual method has also been analyzed. In this paper, we focus … Read more

    The robust stabilization problem for discrete-time descriptor systems

  • Claudiu Dinicu
    • Categories Applications - Science and Engineering, Robust Optimization Tags , ,

    We investigate here the robust stabilization problem for the descriptor discrete time systems and build an optimal solution in the case when both the nominal system and the perturbations are given in terms of left coprime factorizations. Moreover our formulas are given straight from the original data, using solely the stabilizing solutions of two Riccati … Read more

    Maximal Covering Location Problems on networks with regional demand

  • Rafael Blanquero
  • Emilio Carrizosa
  • Boglárka Tóth
    • Categories (Mixed) Integer Nonlinear Programming, Facility Planning and Design, Global Optimization Tags , , , ,

    Covering problems are well studied in the Operations Research literature under the assumption that both the set of users and the set of potential facilities are finite. In this paper we address the following variant, which leads to a Mixed Integer Nonlinear Program (MINLP): locations of p facilities are sought along the edges of a … Read more

    An Inertia-Free Filter Line-Search Algorithm for Large-Scale Nonlinear Programming

  • Naiyuan Chiang
  • Victor M. Zavala
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs, Stochastic Programming Tags , , , ,

    We present a filter line-search algorithm that does not require inertia information about the linear system to ensure global convergence. The proposed approach performs curvature tests along the search step to ensure descent. This feature permits more modularity in the linear algebra, enabling the use of a wider range of iterative and decomposition strategies. We … Read more

    Robust Unit Commitment with Dispatchable Wind: An LP Reformulation of the Second Stage

  • Germán Morales-España
    • Categories Applications - Science and Engineering, Robust Optimization Tags , , ,

    Abstract— The increasing penetration of uncertain generation such as wind and solar in power systems imposes new challenges to the Unit Commitment (UC) problem, one of the most critical tasks in power systems operations. The two most common approaches to address these challenges — stochastic and robust optimization — have drawbacks that prevent or restrict their … Read more

    Semidefinite Optimization Approaches to Applications in Facility Layout and Logistics

  • Philipp Hungerländer
    • Categories Facility Planning and Design, Semi-definite Programming, Transportation

    The main contributions of this thesis are the comparison of existing and the design of new exact approaches based on linear, quadratic and semidefinite relaxations for row layout problems and several applications in logistic. In particular we demonstrate that our suggested semidefinite approach is the strongest exact method to date for most row layout problems. … Read more

    A Semidefinite Optimization Approach to the Parallel Row Ordering Problem

  • Philipp Hungerländer
    • Categories Facility Planning and Design, Linear, Cone and Semidefinite Programming, VLSI layout

    The $k$-Parallel Row Ordering Problem (kPROP) is an extension of the Single-Row Facility Layout Problem (SRFLP) that considers arrangements of the departments along more than one row. We propose an exact algorithm for the kPROP that extends the semidefinite programming approach for the SRFLP by modelling inter-row distances as products of ordering variables. For k=2 … Read more