Extended Karush-Kuhn-Tucker condition for constrained interval optimization problems and its application in support vector machines

Ghosh, Debdas; Singh, Abhishek; Shukla, K. K.; Manchanda, Kartik

doi:10.1016/j.ins.2019.07.017

Cited by 63 publications

(33 citation statements)

References 19 publications

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“…Condition (2), known as the Kuhnna-Tucker theorem [6], defines the optimum point as a point stationary in the coordinate when constraints such as equality are satisfied and the goal function is insensitive to constraints such as inequality. In this simple but important problem, let us trace the meaning of the Lagrange multipliers…”

Section: Methodsmentioning

confidence: 99%

Solution of the Problem of Optimizing Route with Using the Risk Criterion

Mamenko

Zinchenko

Kobets

et al. 2021

Lecture Notes on Data Engineering and Communications Technologies

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The aim of the work is to determine the conditions of optimality in the task of plotting the course of the vessel and the operation of divergence of vessels in conditions of intensive navigation. The need for such work is dictated, firstly, by an increase in the intensity of shipping and, secondly, by the emergence of autonomous ships and transport systems, the traffic control algorithms of which obviously require an optimal approach. The criterion of optimality in problems of this class is the expected risk, one of the components of which is the risk of collision of ships. Based on the analysis of methods for constructing ship divergence algorithms, the task is to find a control algorithm that delivers the best results for all participants in the operation. This formulation of the task greatly facilitates the forecast of the actions of all participants in the discrepancy and is especially expedient in the case of participation in the operation of an autonomous system or a ship with which no contact has been established. Theoretically, the task belongs to the most difficult class of control problems -optimal control of a distributed dynamic system with a vector -a goal functional [3,5,8,[13][14][15]. The ability to obtain a general solution to the task of optimal ship control makes this study expedient.

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Section: Methodsmentioning

confidence: 99%

Solution of the Problem of Optimizing Route with Using the Risk Criterion

Mamenko

Zinchenko

Kobets

et al. 2021

Lecture Notes on Data Engineering and Communications Technologies

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“…Antczak et al [31] studied the optimality conditions and duality results for nonsmooth vector optimization problems with multiple IVFs [32]. In 2019, Ghosh [33] have extended the KKT condition for constrained IVOPs. In addition, Van [34] investigated the duality results for interval-valued pseudoconvex optimization problems with equilibrium constraints.…”

Section: Introductionmentioning

confidence: 99%

Optimality Conditions and Duality for a Class of Generalized Convex Interval-Valued Optimization Problems

Guo

Liu

et al. 2021

Mathematics

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“…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

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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.

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Extended Karush-Kuhn-Tucker condition for constrained interval optimization problems and its application in support vector machines

Cited by 63 publications

References 19 publications

Solution of the Problem of Optimizing Route with Using the Risk Criterion

Solution of the Problem of Optimizing Route with Using the Risk Criterion

Optimality Conditions and Duality for a Class of Generalized Convex Interval-Valued Optimization Problems

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

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