Enumerative techniques for solving some nonconvex global optimization problems

Pardalos, Pãnos M.

doi:10.1007/bf01720032

Cited by 19 publications

(5 citation statements)

References 23 publications

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“…Pardalos [33] discusses a range of enumerative techniques for concave problems based on extreme point ranking. Decomposition techniques have also been applied to this class of problems, see for example [23].…”

Section: Overview Of Existing Methodsmentioning

confidence: 99%

A dynamic programming approach for solving single-source uncapacitated concave minimum cost network flow problems

Fontes

Hadjiconstantinou

Christofides

2006

European Journal of Operational Research

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Section: Overview Of Existing Methodsmentioning

confidence: 99%

A dynamic programming approach for solving single-source uncapacitated concave minimum cost network flow problems

Fontes

Hadjiconstantinou

Christofides

2006

European Journal of Operational Research

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“…E II. Therefore, by (92), min{f(x): x E G} = min{f(xrr): II E S}, (94) so that to solve (P) it suffices to compute the cells II E S for the parametric linear program (S(A)). On the other hand, given the parametric linear prorgam (R(a)) for a E W, the parameter domain W is partitioned into a set n of polyhedrons (cells) each of which, Ll, being associated with an affine mapping X : Ll __,.…”

Section: Special Methods For Special Problemsmentioning

confidence: 99%

D.C. Optimization: Theory, Methods and Algorithms

Tụy

1995

Nonconvex Optimization and Its Applications

159

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“…Among existing optimal methods, cutting-plane and cone-covering [14] provide the most efficient algorithms, but these are usually hard to implement. Enumerative techniques [16] are the most popular, mainly because their implementation is straightforward. We implemented the method of [3].…”

Section: Minimizing Linearly Constrained Concave Functionsmentioning

confidence: 99%

Maximizing Rigidity: Optimal Matching under Scaled-Orthography

Maciel

Costeira

2002

Computer Vision — ECCV 2002

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Abstract. Establishing point correspondences between images is a key step for 3D-shape computation. Nevertheless, shape extraction and point correspondence are treated, usually, as two different computational processes. We propose a new method for solving the correspondence problem between points of a fully uncalibrated scaled-orthographic image sequence. Among all possible point selections and permutations, our method chooses the one that minimizes the fourth singular value of the observation matrix in the factorization method. This way, correspondences are set such that shape and motion computation are optimal. Furthermore, we show this is an optimal criterion under bounded noise conditions. Also, our formulation takes feature selection and outlier rejection into account, in a compact and integrated way. The resulting combinatorial problem is cast as a concave minimization problem that can be efficiently solved. Experiments show the practical validity of the assumptions and the overall performance of the method.

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Enumerative techniques for solving some nonconvex global optimization problems

Cited by 19 publications

References 23 publications

A dynamic programming approach for solving single-source uncapacitated concave minimum cost network flow problems

A dynamic programming approach for solving single-source uncapacitated concave minimum cost network flow problems

D.C. Optimization: Theory, Methods and Algorithms

Maximizing Rigidity: Optimal Matching under Scaled-Orthography

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