Repository – Page 693 – Optimization Online

A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms

Published: 2011/12/16

Laurent Condat

Convex and Nonsmooth Optimization convex and nonsmooth optimization, douglas-rachford method, fenchel-rockafellar duality, forward-backward method, monotone inclusion, monotone operator, operator splitting, primal-dual algorithms, proximal method, saddle point problem

We propose a new first-order splitting algorithm for solving jointly the primal and dual formulations of large-scale convex minimization problems involving the sum of a smooth function with Lipschitzian gradient, a nonsmooth proximable function, and linear composite functions. This is a full splitting approach in the sense that the gradient and the linear operators involved … Read more

Continuous convex sets and zero duality gap for convex programs

Published: 2011/12/15

Convex Optimization constrainedoptimization, continuous convex sets, convexprograms, inner aperture directions, recessionanalysis

This article uses classical notions of convex analysis over euclidean spaces, like Gale & Klee’s boundary rays and asymptotes of a convex set, or the inner aperture directions defined by Larman and Brøndsted for the same class of sets, to provide a new zero duality gap criterion for ordinary convex programs. On this ground, we … Read more

Zero duality gap for convex programs: a general result

Published: 2011/12/15

Convex Optimization constrained optimization, convex optimization, qualification condition

This article addresses a general criterion providing a zero duality gap for convex programs in the setting of the real locally convex spaces. The main theorem of our work is formulated only in terms of the constraints of the program, hence it holds true for any objective function fulfilling a very general qualification condition, implied … Read more

Closed means continuous iff polyhedral: a converse of the GKR theorem

Published: 2011/12/15

Emil Ernst

Convex Optimization closed convex functions, conical points, continuity of convex functions, gale-klee-rockafellar theorem, linearly accessible points, polyhedral points

Given x, a point of a convex subset C of an Euclidean space, the two following statements are proven to be equivalent: (i) any convex function f : C → R is upper semi-continuous at x, and (ii) C is polyhedral at x. In the particular setting of closed convex mappings and Fσ domains, we … Read more

Models for managing the impact of an epidemic

Published: 2011/12/14, Updated: 2012/03/12

Applications - OR and Management Sciences, Biomedical Applications robust optimization, seir

In this paper we consider robust models of surge capacity plans to be deployed in the event of a flu pandemic. In particular, we focus on managing critical staff levels at organizations that must remain operational during such an event. We develop efficient procedures for managing emergency resources so as to minimize the impact of … Read more

Strong formulations for convex functions over nonconvex sets

Published: 2011/12/14, Updated: 2012/12/06

Global Optimization, Nonsmooth Optimization, Second-Order Cone Programming lifting, nonconvex optimization, s-lemma

In this paper we derive strong linear inequalities for sets of the form {(x, q) ∈ R^d × R : q ≥ Q(x), x ∈ R^d − int(P ) }, where Q(x) : R^d → R is a quadratic function, P ⊂ R^d and “int” denotes interior. Of particular but not exclusive interest is the … Read more

On convergence rate of the Douglas-Rachford operator splitting method

Published: 2011/12/13, Updated: 2012/02/03

Convex and Nonsmooth Optimization convergence rate, douglas-rachford operator splitting method

This note provides a simple proof on a O(1/k) convergence rate for the Douglas-Rachford operator splitting method where $k$ denotes the iteration counter. ArticleDownload View PDF

Optimizing the Spectral Radius

Published: 2011/12/12, Updated: 2012/07/08

Control Applications nonnegative matrix, optimization methods, spectral radius, spectrum of a graph

We suggest an approach for finding the maximal and the minimal spectral radius of linear operators from a given compact family of operators, which share a common invariant cone (e.g. for a family of nonnegative matrices). In case of families with so-called product structure, this leads to efficient algorithms for optimizing the spectral radius and … Read more

The Asymmetric Quadratic Traveling Salesman Problem

Published: 2011/12/12

Anja Fischer

(Mixed) Integer Nonlinear Programming, 0-1 Programming, Polyhedra combinatorial optimization, polyhedral combinatorics, quadratic 0-1 programming, reload cost model

The quadratic traveling salesman problem asks for a tour of minimal costs where the costs are associated with each two arcs that are traversed in succession. This structure arises, e. g., if the succession of two arcs represents the costs of loading processes in transport networks or a switch between different technologies in communication networks. … Read more

DC approach to regularity of convex multifunctions with applications to infinite systems

Published: 2011/12/12

Convex and Nonsmooth Optimization, Semi-infinite Programming convex multifunctions, metric regularity, optimization, variational analysis

The paper develops a new approach to the study of metric regularity and related well-posedness properties of convex set-valued mappings between general Banach spaces by reducing them to unconstrained minimization problems with objectives given as the difference of convex (DC) functions. In this way we establish new formulas for calculating the exact regularity bound of … Read more