This paper is devoted to second order necessary optimality conditions for the Mayer optimal control problem when the control set U is a closed subset of R. We show that, in the absence of endpoint constraints, if an optimal control ū(·) is singular and integrable, then for almost every t such that ū(t) is in the interior of U , both the Goh and a generalized LegendreClebsch conditions hold true...

The classical methods for solving initial-boundary-value problems for linear partial differential equations with constant coefficients rely on separation of variables, and specific integral transforms. As such, they are limited to specific equations, with special boundary conditions. Here we review a method introduced by Fokas, which contains the classical methods as special cases. However, thi...

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraint functions need not to be locally Lipschitz. Using Abadie’s qualification convexificators, we provide Karush–Kuhn–Tucker necessary optimality conditions by converting initial problem into bi-criteria optimization problem. Furthermore, establish sufficient under asymptotic convexi...

Motivated by the Maximum Theorem for convex functions (in setting of linear spaces) and subadditive Abelian semigroups), we establish a class generalized functions, i.e., $f:X\to\R$ that satisfy inequality $f(x\circ y)\leq pf(x)+qf(y)$, where $\circ$ is binary operation on $X$ $p,q$ are positive constants. As an application, also obtain extension Karush--Kuhn--Tucker theorem this functions.

In this paper, Karush-Kuhn-Tucker type robust necessary optimality conditions for a nonsmooth interval-valued optimization problem (UCIVOP) are formulated using the concept of LU-optimal solution and generalized Slater constraint qualification (GRSCQ). These shown to be sufficient under convexity. The Wolfe Mond-Weir dual problems over cones convexity assumptions, usual duality results establis...

This paper presents an algorithm for finding the optimal control a current controller that operates as part of system shunt active power filter. The is based upon Karush–Kuhn–Tucker conditions value where signal limited and constraints create cube. explicit solution problem presented simplified calculations are given to lower calculation complexity. compared with classical PI controller. It par...

Abstract The synthetic control method (SCM) represents a notable innovation in estimating the causal effects of policy interventions and programs comparative case study setting. In this paper, we demonstrate that data-driven approach to SCM requires solving bilevel optimization problem. We show how original problem can be solved global optimum through introduction an iterative algorithm rooted ...