Algorithms for quasiconvex minimization

Neto, João Xavier da Cruz; Lopes, J. O.; Travaglia, Marcos V.

doi:10.1080/02331934.2010.528760

Cited by 9 publications

(11 citation statements)

References 17 publications

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“…On the other hand, Proposition 4.3, item 1., extends Theorem 3.1 in [15] and item 3. extends Proposition 7 in [14].…”

Section: The Algorithmsupporting

confidence: 72%

“…In this way, we established an algorithm to find maximal elements. This algorithm extends Algorithm A1 in [14].…”

Section: Discussionmentioning

confidence: 94%

“…If u is quasiconcave and Lipschitz, and possesses a maximum on R n , then f u satisfy assumptions 1., 2. and 3. of our algorithm. In view of this, our algorithm generalizes Algorithm A1 in [14], as we do not require differentiability of u.…”

Section: Ementioning

confidence: 99%

“…In addition, we present an algorithm to obtain these elements, whenever the preference relation is defined on the whole space. This algorithm is inspired by the classical steepest descent method for minimization of quasiconvex functions [14], but instead of the gradient, we use the so-called Plastria-like normal cone of the strict upper contour.…”

Section: Introductionmentioning

confidence: 99%

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Existence and uniqueness of maximal elements for preference relations: Variational approach

Bueno¹,

Cotrina²,

García³

2023

Preprint

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In this work, we reformulate the problem of existence of maximal elements for preference relations as a variational inequality problem in the sense of Stampacchia. Similarly, we establish the uniqueness of maximal elements using a variational inequality problem in the sense of Minty. In both of these approaches, we use the normal cone operator to find existence and uniqueness results, under mild assumptions. In addition, we provide an algorithm for finding such maximal elements, which is inspired by the steepest descent method for minimization. Under certain conditions, we prove that the sequence generated by this algorithm converges to a maximal element.

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“…On the other hand, Proposition 4.3, item 1., extends Theorem 3.1 in [15] and item 3. extends Proposition 7 in [14].…”

Section: The Algorithmsupporting

confidence: 72%

“…In this way, we established an algorithm to find maximal elements. This algorithm extends Algorithm A1 in [14].…”

Section: Discussionmentioning

confidence: 94%

Section: Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Existence and uniqueness of maximal elements for preference relations: Variational approach

Bueno¹,

Cotrina²,

García³

2023

Preprint

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show abstract

“…Since the subgradient method can obtain a search direction at a certain point during optimization, it can be used in convex, quasiconvex and nonconvex problems (Burachik et al, 2010, Neto et al, 2011, Yang et al, 2010. Here the dictionary D can be updated by the subgradient G. That is…”

Section: Discriminative Dictionary Learningmentioning

confidence: 99%

Linear Subspace Learning based on a Learned Discriminative Dictionary for Sparse Coding

Gao¹,

Chen

2013

Proceedings of the International Conference on Computer Vision Theory and Applications

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Learning linear subspaces for high-dimensional data is an important task in pattern recognition. A modern approach for linear subspace learning decomposes every training image into a more discriminative part (MDP) and a less discriminative part (LDP) via sparse coding before learning the projection matrix. In this paper, we present a new linear subspace learning algorithm through discriminative dictionary learning. Our main contribution is a new objective function and its associated algorithm for learning an overcomplete discriminative dictionary from a set of labeled training examples. We use a Fisher ratio defined over sparse coding coefficients as the objective function. Atoms from the optimized dictionary are used for subsequent image decomposition. We obtain local MDPs and LDPs by dividing images into rectangular blocks, followed by blockwise feature grouping and image decomposition. We learn a global linear projection with higher classification accuracy through the local MDPs and LDPs. Experimental results on benchmark face image databases demonstrate the effectiveness of our method.

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Existence and Uniqueness of Maximal Elements for Preference Relations: Variational Approach

Bueno

Cotrina

García

2023

J Optim Theory Appl

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Algorithms for quasiconvex minimization

Cited by 9 publications

References 17 publications

Existence and uniqueness of maximal elements for preference relations: Variational approach

Existence and uniqueness of maximal elements for preference relations: Variational approach

Linear Subspace Learning based on a Learned Discriminative Dictionary for Sparse Coding

Existence and Uniqueness of Maximal Elements for Preference Relations: Variational Approach

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