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On semidefinite bounds for maximization of a non-convex quadratic objective over the l1 unit ball

Mustafa Ç. Pinar, Marc Teboulle (2006)

RAIRO - Operations Research

We consider the non-convex quadratic maximization problem subject to the l1 unit ball constraint. The nature of the l1 norm structure makes this problem extremely hard to analyze, and as a consequence, the same difficulties are encountered when trying to build suitable approximations for this problem by some tractable convex counterpart formulations. We explore some properties of this problem, derive SDP-like relaxations and raise open questions.

On the central paths and Cauchy trajectories in semidefinite programming

Julio López, Héctor Ramírez C. (2010)

Kybernetika

In this work, we study the properties of central paths, defined with respect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a particular case of convex programming with conic constraints. The studied class of functions consists of spectrally defined functions induced by penalty or barrier...

On the quadratic fractional optimization with a strictly convex quadratic constraint

Maziar Salahi, Saeed Fallahi (2015)

Kybernetika

In this paper, we have studied the problem of minimizing the ratio of two indefinite quadratic functions subject to a strictly convex quadratic constraint. First utilizing the relationship between fractional and parametric programming problems due to Dinkelbach, we reformulate the fractional problem as a univariate equation. To find the root of the univariate equation, the generalized Newton method is utilized that requires solving a nonconvex quadratic optimization problem at each iteration. A...

Optimization and Highly Informative Graph Invariants

Dragoš Cvetković, Mirjana Čangalović, Vera Kovačević-Vujčić (2004)

Zbornik Radova

Optimization schemes for wireless sensor network localization

Ewa Niewiadomska-Szynkiewicz, Michał Marks (2009)

International Journal of Applied Mathematics and Computer Science

Many applications of wireless sensor networks (WSN) require information about the geographical location of each sensor node. Self-organization and localization capabilities are one of the most important requirements in sensor networks. This paper provides an overview of centralized distance-based algorithms for estimating the positions of nodes in a sensor network. We discuss and compare three approaches: semidefinite programming, simulated annealing and two-phase stochastic optimization-a hybrid...