We define the inclusion certificate as a measure that expresses each point in the domain of a collection of functions as a convex combination of other points in the domain. Using inclusion certificates, we extend the convex extensions theory to enable simultaneous convexification of functions. We discuss conditions under which the domain of the functions can be reduced without affecting the sim...

This paper is concerned with the minimum-cost flow problem over an arbitrary flow network. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non...

The increasing penetration of the renewable energy sources brings new challenges to frequency security power systems. In order guarantee system security, constraints are incorporated into unit commitment (UC) models. Due non-convex form nadir constraint which makes constrained UC (FCUC) intractable, this letter proposes a revised support vector machine (SVM) based parameter separating plane met...