Necessary and sufficient conditions for a second-order Wiener-Itô integral process to be mixing

Second Order Necessary and Sufficient Optimality Conditions under Abstract Constraints

In this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second order suucient conditions. We show tha...

Necessary and Sufficient Conditions for Unit Graphs to Be Hamiltonian

A graph is Hamiltonian if it has a cycle that visits every vertex exactly once; such a cycle is called a Hamiltonian cycle. In general, the problem of finding a Hamiltonian cycle in a given graph is an NP-complete problem and a special case of the traveling salesman problem. It is a problem in combinatorial optimization studied in operations research and theoretical computer science; see [Garey...

Second-Order Necessary and Sufficient Optimality Conditions for Optimization Problems and Applications to Control Theory

This paper deals with a class of nonlinear optimization problems in a function space, where the solution is restricted by pointwise upper and lower bounds and by finitely many equality and inequality constraints of functional type. Second-order necessary and sufficient optimality conditions are established, where the cone of critical directions is arbitrarily close to the form which is expected...

Necessary and Sufficient Conditions for Differentiating under the Integral Sign

Necessary and sufficient conditions for absolute stability: the case of second-order systems