one of the significant strategies of the power systems is economic dispatch (ed) problem, which is defined as the optimal generation of power units to produce energy at the lowest cost by fulfilling the demand within several limits. the undeniable impacts of ramp rate limits, valve loading, prohibited operating zone, spinning reserve and multi-fuel option on the economic dispatch of practical p...

Using degree theory for countably condensing maps due to Väth, we give an invariance of domain theorem for countably condensing vector fields. The key tool is Borsuk’s theorem for odd countably condensing maps.

Computingmaximum a posteriori (MAP) estimation in graphical models is an important inference problem with many applications. We present message-passing algorithms for quadratic programming (QP) formulations of MAP estimation for pairwise Markov random fields. In particular, we use the concaveconvex procedure (CCCP) to obtain a locally optimal algorithm for the non-convex QP formulation. A simil...

A theorem of Tietze and Nakamija [Ti, N], from 1928, asserts that if a subset X of R is closed, connected, and locally convex, then it is convex. There are many generalizations of this “local to global convexity” phenomenon in the literature. See, e.g., [BF, C, Ka, KW, Kl, SSV, S, Ta]. This paper contains an analogous “local to global convexity” theorem when the inclusion map of X to R is repla...

Let (X, d,m) be a proper, non-branching, metric measure space. We show existence and uniqueness of optimal transport maps for cost written as non-decreasing and strictly convex functions of the distance, provided (X, d,m) satisfies a new weak property concerning the behavior of m under the shrinking of sets to points, see Assumption 1. This in particular covers spaces satisfying the measure con...

In 1975, Yau [Y] proved, by way of a gradient estimate, that a complete manifold M with non-negative Ricci curvature must satisfy the strong Liouville property for harmonic functions. The strong Liouville property (Liouville property) asserts that any positive (bounded) harmonic function defined on M must be identically constant. In 1980, Cheng [C] generalized the gradient estimate to harmonic ...

In this paper particle swarm optimization with smart inertia factor (PSO-SIF) algorithm is proposed to solve combined heat and power economic dispatch (CHPED) problem. The CHPED problem is one of the most important problems in power systems and is a challenging non-convex and non-linear optimization problem. The aim of solving CHPED problem is to determine optimal heat and power of generating u...