A saddle point characterization of efficient solutions for interval optimization problems

Ghosh, Debdulal; Ghosh, Debdas; Bhuiya, Sushil Kumar; Patra, Lakshmi Kanta

doi:10.1007/s12190-017-1140-1

Cited by 29 publications

(18 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Most often [4,14,32,37], IOPs have been analyzed with respect to a partial ordering [20]. Some researchers [3,11] used ordering relations of intervals based on the parametric comparison of intervals. In [7], an ordering relation of intervals is defined by a bijective correspondence between intervals and the points in R 2 .…”

Section: Literature Surveymentioning

confidence: 99%

“…In [7], an ordering relation of intervals is defined by a bijective correspondence between intervals and the points in R 2 . However, these ordering relations [3,11,7] of intervals can be derived from the relations described in [20]. Sengupta et al [30] proposed an acceptability function for intervals, just like a fuzzy membership function.…”

Section: Literature Surveymentioning

confidence: 99%

See 1 more Smart Citation

Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties

Chauhan

Ghosh

Ramík

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

This paper is devoted to the study of gH-Clarke derivative for interval-valued functions. To develop the properties of gH-Clarke derivative, the concepts of limit superior, limit inferior, and sublinear interval-valued functions are studied in the sequel. It is proved that the upper gH-Clarke derivative of a gH-Lipschitz continuous interval- valued function (IVF) always exists. Further, it is found that for a convex and gH-Lipschitz IVF, the upper gH-Clarke derivative coincides with the gH-directional derivative. It is observed that the upper gH-Clarke derivative is a sublinear IVF. Several numerical examples are provided to support the study.

show abstract

Section: Literature Surveymentioning

confidence: 99%

Section: Literature Surveymentioning

confidence: 99%

Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties

Chauhan

Ghosh

Ramík

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the literature of IOP, there are various techniques and theorems for obtaining the solutions to IOPs (see [3,5,8,10,11,12,19,20,22,23,34]). Ishibuchi and Tanaka [19] proposed a method to solve linear IOPs, which is subsequently generalized in [7].…”

Section: Literature Surveymentioning

confidence: 99%

Generalized-Hukuhara Subgradient Method for Optimization Problem with Interval-valued Functions and its Application in Lasso Problem

Ghosh¹,

Debnath²,

Mesiar³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

In this study, a gH-subgradient technique is developed to obtain efficient solutions to the optimization problems with nonsmooth nonlinear convex interval-valued functions. The algorithmic implementation of the developed gH-subgradient technique is illustrated. As an application of the proposed gH-subgradient technique, an 1 penalized linear regression problem, known as a lasso problem, with interval-valued features is solved.

show abstract

“…In 2016, Singh et al [33] proposed the concept of Pareto optimal solution for the interval-valued multi-objective programming problems. Many other researchers have also proposed optimality conditions and solution concepts for IOPs, see for instance [1,12,15,16,35] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Weak Sharp Minima for Interval-Valued Functions and its Primal-Dual Characterizations Using Generalized Hukuhara Subdifferentiability

Kumar

Ghosh

Kumar

2021

Preprint

Self Cite

View full text Add to dashboard Cite

This article introduces the concept of weak sharp minima (WSM) for convex interval-valued functions (IVFs). To identify a set of WSM of a convex IVF, we provide its primal and dual characterizations. The primal characterization is given in terms of gHdirectional derivatives. On the other hand, to derive dual characterizations, we propose the notions of the support function of a subset of I(R) n and gH-subdifferentiability for convex IVFs. Further, we develop the required gH-subdifferential calculus for convex IVFs. Thereafter, by using the proposed gH-subdifferential calculus, we provide dual characterizations for the set of WSM of convex IVFs.

show abstract

A saddle point characterization of efficient solutions for interval optimization problems

Cited by 29 publications

References 21 publications

Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties

Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties

Generalized-Hukuhara Subgradient Method for Optimization Problem with Interval-valued Functions and its Application in Lasso Problem

Weak Sharp Minima for Interval-Valued Functions and its Primal-Dual Characterizations Using Generalized Hukuhara Subdifferentiability

Contact Info

Product

Resources

About