‎In this paper‎, ‎some KKT type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (MINPP) are established‎. ‎We achieve‎ ‎this by employing a Lagrange function for MINPP‎. ‎In addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

In a seminal paper “Volumen und Oberfläche” (1903), Minkowski introduced the basic notion of mixed volumes and corresponding inequalities that lie at heart convex geometry. The fundamental importance characterizing extremals these was already emphasized by himself, but has to date only been resolved in special cases. this paper, we completely settle Minkowski’s quadratic inequality, confirming ...

We extend results proven by the second author ([Oh]) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spacesX with curvature bounded below: the gradient flow of a geodesically convex functional on the quadratic Wasserstein space (P(X),W2) satisfies the evolution variational inequality. Moreover, the gradient flow enjoys uniqueness and contractivity. These results are obt...

In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...

We show that Artin groups of finite type satisfy a quadratic isoperimetric inequality. Moreover we describe an explicit algorithm to solve the word problem in quadratic time.

We consider the extended trust region subproblem (eTRS) as the minimization of an indefinite quadratic function subject to the intersection of unit ball with a single linear inequality constraint. Using a variation of the S-Lemma, we derive the necessary and sufficient optimality conditions for eTRS. Then, an OCP/SDP formulation is introduced for the problem. Finally, several illustrative examp...