let $g=(v,e)$ be a simple graph. a set $dsubseteq v$ is adominating set of $g$ if every vertex in $vsetminus d$ has atleast one neighbor in $d$. the distance $d_g(u,v)$ between twovertices $u$ and $v$ is the length of a shortest $(u,v)$-path in$g$. an $(u,v)$-path of length $d_g(u,v)$ is called an$(u,v)$-geodesic. a set $xsubseteq v$ is convex in $g$ ifvertices from all $(a, b)$-geodesics belon...

let $g=(v,e)$ be a simple graph. a set $dsubseteq v$ is adominating set of $g$ if every vertex in $vsetminus d$ has atleast one neighbor in $d$. the distance $d_g(u,v)$ between twovertices $u$ and $v$ is the length of a shortest $(u,v)$-path in$g$. an $(u,v)$-path of length $d_g(u,v)$ is called an$(u,v)$-geodesic. a set $xsubseteq v$ is convex in $g$ ifvertices from all $(a, b)$-geodesics belon...

In many real-world applications, unlabeled examples are inexpensive and easy to obtain. Semi-supervised approaches try to utilize such examples to boost the predictive performance. But previous research mainly focuses on classification problem, and semi-supervised regression remains largely under-studied. In this work, a novel semi-supervised regression method, semi-supervised LS-SVR (S2LS-SVR)...

We present a generalization of the Phelps lemma to locally convex topological vector spaces and show the equivalence of this theorem, Ekeland's principle and Dane s' drop theorem in locally convex spaces to their Banach space counterparts and to a Pareto eeciency theorem due to Isac. Concerning the drop theorem this solves a problem proposed by G. Isac in 1997. We show that another formulation ...

An Ostrowski type inequality for general convex functions defined on linear spaces is generalised. Some inequalities which improve the HermiteHadamard type inequality for convex functions defined on linear spaces are derived using the obtained result. The results in normed linear spaces are used to obtain some inequalities which are related to the given norm and associated semi-inner products, ...

The purpose of this paper is to characterize the Banach spaces and the locally convex spaces E for which bounded additive measures or bounded σadditive measures with values in L(E, F ), the space of continuous linear maps from E into F , are of bounded semi-variation for any Banach space or locally convex space F . This paper gives an answer to a problem posed by D.H. Tucker in [6].

A graph-based classification method is proposed both for semi-supervised learning in the case of Euclidean data and for classification in the case of graph data. Our manifold learning technique is based on a convex optimization problem involving a convex regularization term and a concave loss function with a trade-off parameter carefully chosen so that the objective function remains convex. As ...

In this semi-tutorial paper, the positioning problem is formulated as a convex feasibility problem (CFP). To solve the CFP for non-cooperative networks, we consider the well-known projection onto convex sets (POCS) technique and study its properties for positioning. We also study outer-approximation (OA) methods to solve CFP problems. We then show how the POCS estimate can be upper bounded by s...

Convexification is a fundamental technique in (mixed-integer) nonlinear optimization and many convex relaxations are parametrized by variable bounds, i.e., the tighter the bounds, the stronger the relaxations. This paper studies how bound tightening can improve convex relaxations for power network optimization. It adapts traditional constraintprogramming concepts (e.g., minimal network and boun...

The multiple load structural topology design problem is modeled as a minimization of the weight of the structure subject to equilibrium constraints and restrictions on the local stresses and nodal displacements. The problem involves a large number of discrete design variables and is modeled as a non-convex mixed 0–1 program. For this problem, several convex and mildly non-convex continuous rela...