Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems

Bouhamidi, A.; Bellalij, M.; Enkhbat, Rentsen; Jbilou, Khalide; Raydan, Marcos

doi:10.1007/s10957-017-1203-3

Cited by 4 publications

(8 citation statements)

References 21 publications

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“…For this problem, we first provide local necessary conditions and then obtain a verifiable sufficient condition for identifying global minimizer among the local ones. In this regard, our problem generalizes the cases considered in [20,23] and [2] in a considerable way.…”

Section: Introductionmentioning

confidence: 85%

“…In [23] a quadratic fractional optimization problem has been studied with two quadratic convex constraints using the classical Dinkelbach approach with no global convergence guarantee. In [2], using the conditional gradient method the ratio of two convex functions over a closed and convex set has been studied numerically. In this article we consider the problem MP when f j : j = 0, 1, 2, .…”

Section: Introductionmentioning

confidence: 99%

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Lagrange Multiplier Local Necessary and Global Sufficiency Criteria for Some Non-Convex Programming Problems

Muraleetharan,

Selvarajan,

Srisatkunarajah

et al. 2018

Preprint

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In this paper we consider three minimization problems, namely quadratic, ρ-convex and quadratic fractional programing problems. The quadratic problem is considered with quadratic inequality constraints with bounded continuous and discrete mixed variables. The ρ-convex problem is considered with ρ-convex inequality constraints in mixed variables. The quadratic fractional problem is studied with quadratic fractional constraints in mixed variables. For all three problems we reformulate the problem as a mathematical programming problem and apply standard Karush Kuhn Tucker necessary conditions. Then, for each problem, we provide local necessary optimality condition. Further, for each problem a Lagrangian multiplier sufficient optimality condition is provided to identify global minimizer among the local minimizers. For the quadratic problem underestimation of a Lagrangian was employed to obtain the desired sufficient conditions. For the ρ-convex problem we obtain two sufficient optimality conditions to distinguish a global minimizer among the local minimizers, one with an underestimation of a Lagrangian and the other with a different technique. A global sufficient optimality condition for the quadratic fractional problem is obtained by reformulating the problem as a quadratic problem and then utilizing the results of the quadratic problem. Examples are provided to illustrate the significance of the results obtained.

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Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Lagrange Multiplier Local Necessary and Global Sufficiency Criteria for Some Non-Convex Programming Problems

Muraleetharan,

Selvarajan,

Srisatkunarajah

et al. 2018

Preprint

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“…In this subsection, we present a noteworthy extension of the gradient descent method tailored for addressing the general tensorial convex minimization problem (1.1). The literature has seen diverse adaptations of the gradient descent technique to tackle various minimization problems, including nonlinear minimization problems [16], fractional optimization problems [4], among others. The proximal gradient method serves as a generalized version of the gradient descent method, particularly adept at handling non-differentiability in the cost function; see r2, 3, 20, 32s.…”

Section: Preliminaries and Notationmentioning

confidence: 99%

N-mode Minimal Tensor Extrapolation Methods

Bentbib

Jbilou

Tahiri

2023

Preprint

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The purpose of this work is to present, using the n-mode product, a new approach to generalize, for tensor sequence,s the well-known vector extrapolation methods MPE ( Minimal Polynomial Extrapolation method) and RRE (Reduced Rank Extrapolation method). We define the notion of the n-mode minimal polynomial of a matrix with respect to a tensor. This polynomial will be used, through the iterative solution of some tensor linear systems, to introduce the tensor version of MPE and RRE. These methods involve only the terms of sequences that result from the used iterative methods. The implementation of these methods on some sequences of tensors confirms the effectiveness and applicability of our approach.

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“…where Ω is a convex nonempty bounded set. As F and G are proper lower semicontinuous convex functions, F is Gateau differentiable and uniformly convex on X and if it is further assumed that Ω is closed, then, there exists a unique solution of the minimization problem (5), see [2,41,13,21,15] for a deeper discussion.…”

Section: Problemmentioning

confidence: 99%

“…fractional optimization problems [5] and others. The proximal gradient method represents a generalized form of the gradient descent method in the presence of non differentiability in the cost function [1,2,40,41].…”

Section: Tensorial Double Proximal Gradient Algorithmmentioning

confidence: 99%

An Accelerated Tensorial Double Proximal Gradient Method for Total Variation Regularization Problem

Benchettou

Bentbib

Bouhamidi

2023

J Optim Theory Appl

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Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems

Cited by 4 publications

References 21 publications

Lagrange Multiplier Local Necessary and Global Sufficiency Criteria for Some Non-Convex Programming Problems

Lagrange Multiplier Local Necessary and Global Sufficiency Criteria for Some Non-Convex Programming Problems

N-mode Minimal Tensor Extrapolation Methods

An Accelerated Tensorial Double Proximal Gradient Method for Total Variation Regularization Problem

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