Optimality conditions and duality for interval-valued optimization problems using convexifactors

Abstract

This paper is devoted to the applications of convexifactors on interval-valued programming problem. Based on the concept of LU optimal solution, sufficient optimality conditions are established under generalized ∂ * -convexity assumptions. Furthermore, appropriate duality theorems are derived for two types of dual problem, namely Mond-Weir and Wolfe type duals. We also construct examples to manifest the established relations.

Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem

“…For that we have defined the notions of asymptotic pseudoconvex and asymptotic quasiconvex functions in terms of convexifactors. Convexifactors given by Demyanov [11] are further studied by Jeyakumar and Luc [17], Dutta and Chandra [13,14], Li and Zhang [24], Luu [25], Suneja and Kohli [30,31,32], Kabgani and Soleimani-damaneh [18,20], Kabgani et al [19], Jayswal et al [15,16], Ahmad et al [1] and others. These convexifactors are always closed sets but not necessarily convex or compact.…”

Duality results for interval-valued pseudoconvex optimization problem with equilibrium constraints with applications

“…Based on the fact that necessary and sufficient optimality conditions for the local LU -optimal solution of constrained interval-valued optimization problems were well known in many literature, e.g., in Panda (2015, 2016), Jayswal et al (2011Jayswal et al ( , 2016, Wu (2008), Luu and Mai (2018), and the obtained results for the local efficient solution types of vector equilibrium problems, e.g., in Gong (2010), Luu and Hang (2015); Luu and Su (2018), our main aim here is to construct the two Wolfe and Mond-Weir dual models for the intervalvalued pseudoconvex optimization problem with equilibrium constraints (IOPEC) in terms of contingent epiderivatives. Given a feasible vector x ∈ K , we denote the following index sets:…”

“…Extending the concept of lower-upper (in short, LU) optimal solution in Wu (2008), and as well as in Jayswal et al (2011), we may receive the notion of lower-upper optimal solution to the interval-valued optimization problems with constraints, even in any vector optimization problem with equilibrium constraints. Based on the fact that the class of interval-valued nonlinear programming problems has been extensively studied on optimality and duality by many researchers in recent years, e.g., in Bhurjee and Panda (2015), Bhurjee and Panda (2016), Bot and Grad (2010), Jayswal et al (2011), Jayswal et al (2016), Luu and Mai (2018), More (1983), Wu (2008) and the construction of Wolfe and Mond-Weir dual models to these has not been established yet, we continue to study and develop these result on optimality and duality to the interval-valued optimization problem with equilibrium constraints and an application of the obtained results for these dual models will be presented in the literature.…”

“…There are many tools which involving generalized derivatives have been used for establishing optimality conditions and as well as strong and weak duality theorems in constrained interval-valued optimization problems. For example, under suitable assumptions on convexificators, Jayswal et al (2016) obtained duality and optimality conditions for the interval-valued nonlinear programming problems without constraints in finite-dimensional spaces. More recently, Luu and Mai (2018) gave Fritz John and Karush-Kuhn-Tucker necessary and sufficient optimality conditions for the local lower-upper optimal solution of interval-valued optimization problem with set, inequality and equality constraints with locally Lipschitz functions and regular functions in the sense of Clarke.…”

Interval‐valued variational programming problem with Caputo–Fabrizio fractional derivative

“…Bhurjee and Panda [4] proposed a framework for investigating interval-valued optimization problems in their recent research. In order to understand the fundamentals of interval-valued optimization, we recommend reading the books [5][6][7][8][9] and some current articles [4,[10][11][12][13][14][15][16].…”