Displaying similar documents to “New technique for solving univariate global optimization”

État de l'art des méthodes “d'optimisation globale”

Gérard Berthiau, Patrick Siarry (2010)

RAIRO - Operations Research

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We present a review of the main “global optimization" methods. The paper comprises one introduction and two parts. In the introduction, we recall some generalities about non linear constraint-less optimization and we list some classifications which have been proposed for the global optimization methods. We then describe, in the first part, various “classical" global optimization methods, most of which available long before the appearance of Simulated Annealing (a key event in this...

Diagonal Numerical Methods for Solving Lipschitz Global Optimization Problems

Dmitri E. Kvasov (2008)

Bollettino dell'Unione Matematica Italiana

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This paper briefly describes some results of the author's PhD thesis, which has been specially mentioned by the Italian INdAM-SIMAI Committee for the Competition "The Best PhD Thesis in Applied Mathematics defended in 2004-2006". In this work, a global optimization problem is considered where the objective function is a multidimensional black-box function satisfying the Lipschitz condition over a hyperinterval and hard to evaluate. Such functions are frequently encountered in practice...

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

Mustafa Ç. Pinar, Marc Teboulle (2006)

RAIRO - Operations Research

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We consider the non-convex quadratic maximization problem subject to the unit ball constraint. The nature of the 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.

Unified global optimality conditions for smooth minimization problems with mixed variables

Vaithilingam Jeyakumar, Sivakolundu Srisatkunarajah, Nguyen Quang Huy (2008)

RAIRO - Operations Research

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In this paper we establish necessary as well as sufficient conditions for a given feasible point to be a global minimizer of smooth minimization problems with mixed variables. These problems, for instance, cover box constrained smooth minimization problems and bivalent optimization problems. In particular, our results provide necessary global optimality conditions for difference convex minimization problems, whereas our sufficient conditions give easily verifiable conditions for global...

Multi-objective Optimization Problem with Bounded Parameters

Ajay Kumar Bhurjee, Geetanjali Panda (2014)

RAIRO - Operations Research - Recherche Opérationnelle

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In this paper, we propose a nonlinear multi-objective optimization problem whose parameters in the objective functions and constraints vary in between some lower and upper bounds. Existence of the efficient solution of this model is studied and gradient based as well as gradient free optimality conditions are derived. The theoretical developments are illustrated through numerical examples.

Modifications of the limited-memory BFGS method based on the idea of conjugate directions

Vlček, Jan, Lukšan, Ladislav

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Simple modifications of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections of the used difference vectors (derived from the idea of conjugate directions), utilizing information from the preceding iteration. For quadratic objective functions, the improvement of convergence is the best one in some sense and all stored difference vectors are conjugate for unit stepsizes. The algorithm is globally convergent for...