In this paper we consider the class of polynomial optimization problems with inequality and equality constraints, in which every problem of the class is obtained by perturbations of the objective function, while the constraint functions are kept fixed. Under certain assumptions, we establish some stability properties (e.g., strong Hölder stability with explicitly determined exponents, semiconti...

In this paper, we defined the interval form of \(\alpha, \beta\) level set for triangular q-rung orthopair fuzzy (qROPF) number. To obtain a differentiability notion qROPF valued functions, Hukuhara (H-differentiability) and level-wise H-differentiability is defined. Using KKT optimality condition optimization problem with objective function are formulated.

Our approach to the Karush-Kuhn-Tucker theorem in [OSC] was entirely based on subdifferential calculus (essentially, it was an outgrowth of the two subdifferential calculus rules contained in the Fenchel-Moreau and Dubovitskii-Milyutin theorems, i.e., Theorems 2.9 and 2.17 of [OSC]). On the other hand, Proposition B.4(v) in [OSC] gives an intimate connection between the subdifferential of a fun...

Abstract This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly efficient solutions of the considered problem. These are presented in terms Karush-Kuhn-Tucker multipliers and convexificators related Examples illustrating our find...

We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui and his colleagues have propose 'SAFE' rules, based on univariate inner products between each predictor and the outcome, which guarantee that a coefficient will be 0 in the solution vector. This provides a reduction in the number of variables that need to be entered into...

This paper is devoted to provide sufficient Karush Kuhn Tucker (in short, KKT) conditions of optimality second-order for a set-valued fractional minimax problem. In addition, we define duals the types Mond-Weir and Wolfe Further obtain theorems duality under contingent epi-derivative together with generalized cone convexity suppositions second-order.

In this paper, by considering the parametric technique, we study a class of fractional optimization problems involving data uncertainty in objective functional. We formulate and prove robust Karush-Kuhn-Tucker necessary optimality conditions provide their sufficiency convexity and/or concavity assumptions involved functionals. addition, to complete study, an illustrative example is presented.

Bilevel programming problems are often reformulated using the Karush-Kuhn-Tucker conditions for lower level problem resulting in a mathematical program with complementarity constraints (MPCC). First, we present KKT reformulation of bilevel optimization on Riemannian manifolds. Moreover, show that global optimal solutions theMPCCcorrespond to manifolds provided convex satisfies Slater?s constrai...