A Polynomial Time Constraint-Reduced Algorithm for Semidefinite Optimization Problems, with Convergence Proofs

  • Dianne P. O'Leary
  • Sungwoo Park
    • Categories Semi-definite Programming Tags , , , , , , , , ,

    We present an infeasible primal-dual interior point method for semidefinite optimization problems, making use of constraint reduction. We show that the algorithm is globally convergent and has polynomial complexity, the first such complexity result for primal-dual constraint reduction algorithms for any class of problems. Our algorithm is a modification of one with no constraint reduction … Read more

    A Flexible Inexact Restoration Method and Application to Optimization with Multiobjective Constraints under Weighted-Sum Scalarization

  • Luís Felipe Bueno
  • Gabriel Haeser
  • José Mario Martínez
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization

    We introduce a new flexible Inexact-Restoration (IR) algorithm and an application to problems with multiobjective constraints (MOCP) under the weighted-sum scalarization approach. In IR methods each iteration has two phases. In the first phase one aims to improve the feasibility and, in the second phase, one minimizes a suitable objective function. This is done in … Read more

    A Semidefinite Hierarchy for Containment of Spectrahedra

  • Kai Kellner
  • Thorsten Theobald
  • Christian Trabandt
    • Categories Semi-definite Programming Tags , , , , ,

    A spectrahedron is the positivity region of a linear matrix pencil, thus defining the feasible set of a semidefinite program. We propose and study a hierarchy of sufficient semidefinite conditions to certify the containment of a spectrahedron in another one. This approach comes from applying a moment relaxation to a suitable polynomial optimization formulation. The … Read more

    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

    A Short Proof of Strassen’s Theorem Using Convex Analysis

  • Benjamin Armbruster
    • Categories Stochastic Programming Tags

    We give a simple proof of Strassen’s theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and provides an additional, intuitive optimization formulation for stochastic dominance. CitationNorthwestern Univ., Aug., 2013ArticleDownload View PDF

    Practical Portfolio Optimization

  • Isaac Siwale
    • Categories Applications - OR and Management Sciences, Finance and Economics

    This paper is on the portfolio optimization problem for which two generic models are presented in the context of a proprietary solver called GENO: the first is a pseudo-dynamic model meant for the single holding-period case; the second is a truly dynamic model that applies to both the single and the multi-period scenario. Both models … 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

    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