We contribute to fulfill the long-lasting gap in understanding of spatial search with multiple marked vertices. The theoretical framework is that discrete-time quantum walks (QW), i.e., local unitary matrices drive evolution a single particle on lattice. QW based algorithms are well understood when they have tackle fundamental problem finding only one element $d\text{\ensuremath{-}}\text{dimens...

In this paper, we are concerned with a fractional multiobjective optimization problem ( P ). Using support functions together generalized Guignard constraint qualification, give necessary optimality conditions in terms of convexificators and the Karush–Kuhn–Tucker multipliers. Several intermediate problems have been introduced to help us our investigation.

This paper focuses on second-order necessary optimality conditions for constrained optimization problems Banach spaces. For in the classical setting, where objective function is $$C^2$$ -smooth, we show that strengthened are valid if constraint set generalized polyhedral convex. a new just assumed to be $$C^1$$ -smooth and convex, establish sharp based Fréchet subdifferential of tangent set. Th...

This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our consists reducing problem (nondynamic) optimization normed space and then applying the results recently obtained latter class by using generalized differentiation. In this way, we derive nonconvex calculus ...

In this paper, we give optimality conditions for the quadratic programming problems with constraints defined by finitely many convex in Hilbert spaces. As special cases, obtain under linear

Sequential optimality conditions for constrained optimization are necessarily satisfied by local minimizers, independently of the fulfillment of constraint qualifications. These conditions support the employment of different stopping criteria for practical optimization algorithms. On the other hand, when an appropriate strict constraint qualification associated with some sequential optimality c...

Abstract. The study of fractional variational problems in terms of a combined fractional Caputo derivative is introduced. Necessary optimality conditions of Euler–Lagrange type for the basic, isoperimetric, and Lagrange variational problems are proved, as well as transversality and sufficient optimality conditions. This allows to obtain necessary and sufficient Pareto optimality conditions for ...

In this paper sufficient second order optimality conditions for optimal control problems subject to stationary variational inequalities of obstacle type are derived. Since optimality conditions for such problems always involve measures as Lagrange multipliers, which impede the use of efficient Newton type methods, a family of regularized problems is introduced. Second order sufficient optimalit...