Concepts for Approximate Solutions of Vector Optimization Problems with Variable Order Structures

Soleimani, Behnam; Tammer, Christiane

doi:10.1007/s10013-014-0103-1

Cited by 14 publications

(4 citation statements)

References 34 publications

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“…The decision-maker must choose the parameters, as they are not predetermined. Making this choice can pose significant challenges or become impossible for some problems [27][28][29]. Consequently, to overcome these drawbacks, some descent-based algorithms have been suggested as solution approaches for VOP.…”

Section: Vopmentioning

confidence: 99%

Spectral-like conjugate gradient methods with sufficient descent property for vector optimization

Yahaya,

Kumam,

Salisu

et al. 2024

PLoS ONE

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Several conjugate gradient (CG) parameters resulted in promising methods for optimization problems. However, it turns out that some of these parameters, for example, ‘PRP,’ ‘HS,’ and ‘DL,’ do not guarantee sufficient descent of the search direction. In this work, we introduce new spectral-like CG methods that achieve sufficient descent property independently of any line search (LSE) and for arbitrary nonnegative CG parameters. We establish the global convergence of these methods for four different parameters using Wolfe LSE. Our algorithm achieves this without regular restart and assumption of convexity regarding the objective functions. The sequences generated by our algorithm identify points that satisfy the first-order necessary condition for Pareto optimality. We conduct computational experiments to showcase the implementation and effectiveness of the proposed methods. The proposed spectral-like methods, namely nonnegative SPRP, SHZ, SDL, and SHS, exhibit superior performance based on their arrangement, outperforming HZ and SP methods in terms of the number of iterations, function evaluations, and gradient evaluations.

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Section: Vopmentioning

confidence: 99%

Spectral-like conjugate gradient methods with sufficient descent property for vector optimization

Yahaya,

Kumam,

Salisu

et al. 2024

PLoS ONE

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“…We denote by (ε, c)−WMin (A, K) the set of all weak εc−minimal elements of A with respect to K, by (ε, c) − WNond (A, K) the set of all weak εc−nondominated elements of A with respect to K and by (ε, c) − WRob (A, K) the set of all weak εc−robust elements of A with respect to K. For the concepts in Definition 3.1 we use the same corresponding notations without mentioning (ε, c) . For more details on properties of the minimality concepts above and differences between them, see, for example, [9,11,12].…”

Section: Stability Of Approximate Efficiencymentioning

confidence: 99%

Approximate efficiency in set-valued optimization with variable order

2022

J. Nonlinear Var. Anal.

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We consider constrained set-valued optimization problems with variable order in view of two main purposes: one is to deduce conditions for stability of minima of such problems at the perturbations of the objective map and the set of constraints, and the second is to study some possibilities of recovering optimization problems with fixed order. We apply our results in order to obtain optimality conditions for such problems. The main tools we use are four types of cone enlargements.

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“…Our motivation is its application to career development theories; in particular, changing job process. Using the recent variational rationality approach of human dynamics, which focuses the attention on the main concept of worthwhile move [45,46,47,48,49], we can give an intuitive answer to the initial question: "why changing job can be hard?" which happens as long as motivation to change job is not high enough with respect to resistance to change job.…”

Section: Introductionmentioning

confidence: 99%

Variational principles in set optimization with domination structures and application to changing jobs

2019

J. Appl. Numer. Optim.

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Dedicated to Professor Christiane Tammer on her 60th birthday.Abstract. This paper is devoted to new versions of Ekeland's variational principle in set optimization with domination structure, where set optimization is an extension of vector optimization from vector-valued functions to set-valued maps using Kuroiwa's set-less relations to compare one entire image set with another whole image set, and where domination structure is an extension of ordering cone in vector optimization; it assigns each element of the image space to its own domination set. We use Gerstewitz's nonlinear scalarization function to convert a set-valued map into an extended real-valued function and the idea of the proof of Dancs-Hegedüs-Medvegyev's fixed-point theorem. Our setting is applicable to dynamic processes of changing jobs in which the cost function does not satisfy the symmetry axiom of metrics and the class of set-valued maps acting from a quasimetric space into a real linear space. The obtained result is new even in simpler settings.

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Concepts for Approximate Solutions of Vector Optimization Problems with Variable Order Structures

Cited by 14 publications

References 34 publications

Spectral-like conjugate gradient methods with sufficient descent property for vector optimization

Spectral-like conjugate gradient methods with sufficient descent property for vector optimization

Approximate efficiency in set-valued optimization with variable order

Variational principles in set optimization with domination structures and application to changing jobs

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