Nonsmooth ρ − (η, θ)-invexity in multiobjective programming problems

Abstract

In this paper we extend Reiland's results for a nonlinear (single objective) optimization problem involving nonsmooth Lipschitz functions to a nonlinear multiobjective optimization problem (MP) for ρ − (η, θ )-invex functions. The generalized form of the Kuhn-Tucker optimality theorem and the duality results are established for (MP).

Sufficiency and Duality for Multiobjective Programming under New Invexity

“…For example, we can see [10][11][12]. In particular, Nahak and Mohapatra [13] introduced the concept of -( , )-invexity function and discussed a class of multiobjective programming problems by using the new generalized functions. Padhan and Nahak [14] introduced higher-order -( , )-invexity functions for studying two different pairs of higher-order symmetric dual programs.…”

Efficiency in Multiobjective Programming with Generalized Invexity

“…  pseudoinvex-I at x with respect to  , the inequality (4) follows : (5)- (6) and (3), with ( , ) 0 , ( , ) 0 Which contradicts (7). Therefore x is a weakly efficient solution of (MP).…”

“…Gao [4] introduced B -(p, r) -V -type I Functions and Antczakk [5] given a class of ( , ) B p r  invex functions. For details, the readers are advised to consult other similar literatures [6][7][8].…”

Sufficiency in Multiobjective Programming under Second-orderB- (p,r) -V- type I Functions

“…Many generalized convex functions have been exploited in considerable details. See, for example, [3][4][5][6][7] and the references cited therein. To date, many authors investigated the optimality conditions and duality results for the optimization programming problems under the generalized convexity assumption.…”