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Covering graphs with convex sets and partitioning graphs into convex sets
(Elsevier Science, 2020-06)
We present some complexity results concerning the problems of covering a graph with p convex sets and of partitioning a graph into p convex sets. The following convexities are considered: digital convexity, monophonic ...
Convex p-partitions of bipartite graphs
(Elsevier, 2016)
A set of vertices X of a graph G is convex if no shortest path between two vertices in X contains a vertex outside X. We prove that for fixed p >= 1, all partitions of the vertex set of a bipartite graph into p convex sets ...
Sets of probability distributions, independence, and convexity
(SPRINGERDORDRECHT, 2012)
This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of "convex Bayesianism" (in particular ...
A pair of matrices sharing common Lyapunov solutions - A closer look
(Elsevier Science IncNew YorkEUA, 2003)
Subdifferential of the Supremum via Compactification of the Index Set
(Springer, 2020)
We give new characterizations for the subdifferential of the supremum of an arbitrary family of convex functions, dropping out the standard assumptions of compactness of the index set and upper semi-continuity of the ...
Differentially Private Stochastic Optimization: New Results in Convex and Non-Convex Settings
(2021)
We study differentially private stochastic optimization in convex and non-convex settings. For the convex case, we focus on the family of non-smooth generalized linear losses (GLLs). Our algorithm for the $\ell_2$ setting ...
Characterization of tropical hemispaces by (P,R)-decompositions
(Elsevier, 2014-01)
We consider tropical hemispaces, defined as tropically convex sets whose complements are also tropically convex, and tropical semispaces, defined as maximal tropically convex sets not containing a given point. We introduce ...
Algorithms for Maximum Independent Set in Convex Bipartite Graphs
(SPRINGER, 2009)
A bipartite graph G = (V, W, E) is convex if there exists an ordering of the vertices of W such that, for each v. V, the neighbors of v are consecutive in W. We describe both a sequential and a BSP/CGM algorithm to find a ...
Mixed-integer convex model for VAr expansion planning
(Ieee, 2014-01-01)
This paper presents a mixed-integer convex-optimization-based approach for optimum investment reactive power sources in transmission systems. Unlike some convex-optimization techniques for the reactive power planning ...
Mixed-integer convex model for VAr expansion planning
(2014-01-01)
This paper presents a mixed-integer convex-optimization-based approach for optimum investment reactive power sources in transmission systems. Unlike some convex-optimization techniques for the reactive power planning ...