Abstract We consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. prove that equilateral triangle is local maximiser of lowest eigenvalue among all triangles given area provided negative parameter sufficiently small in absolute value, with smallness depending only. Moreover, using various trial functions, we obtain sufficient conditions for global optimal...

In this paper, we study a nonconvex quadratic minimization problem with two constraints, one of which being convex. We introduce convex relaxations (CQRs) and discuss cases, where the is equivalent to exactly CQRs. Particularly, show that global optimal solution can be recovered from an Through equivalence, new conditions under enjoys strong Lagrangian duality, generalizing recent condition in ...

This paper deals with semi-infifinite programming multiple fuzzy-valued objective functions. Firstly, some types of effificient solutions are proposed and illustrated in examples. Then, necessary suffificient Karush-Kuhn-Tucker optimality conditions for functions established.

⎯The convexity assumptions for a minimax fractional programming problem of variational type are relaxed to those of a type I and related functions. Sufficient optimality conditions are established under the aforesaid assumptions. Several duality theorems are obtained for Wolfe type and Mond-Weir type duals and the original problem. Keyword⎯Minimax programming; Fractional programming; Sufficient...