Using polarity, we give an outer polyhedral approximation for the epigraph of set functions. For a submodular function, prove that corresponding polar relaxation is exact; hence, it equivalent to Lovász extension. The approach provides alternative proof convex hull description function. Computational experiments show inequalities from approximations can be effective as cutting planes solving we...

The outage of power system equipment is one the most important factors that affect reliability and economy system. It crucial to consider influence contingencies elaborately in planning problem. In this paper, a distributionally robust transmission expansion model proposed which uncertainty contingency probability considered. described by interval based on rate single equipment. An epigraph ref...

Believing, with Max Weber, that man is an animal suspended in webs of significance he himself has spun, I take culture to be those webs, and the analysis it therefore not experimental science search law but interpretive one meaning. (Geertz 1973, p. 5) In this well-known quotation featured here as epigraph, defined a web meanings humans weave hold themselves up and, can assume, provide panorami...

We consider the DC optimization problem (P) inf x∈X {(f1(x) − f2(x)) + (g1(Ax) − g2(Ax))}, where f1, f2, g1 and g2 are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y respectively, and A is a linear continuous operator from X to Y . Adopting the standard convexification technique, a Fenchel dual problem of (P) is given. By using properties of the ep...

Abstract We consider minimization problems with bisubmodular objective functions. propose valid inequalities, namely the poly-bimatroid and provide a complete linear description of convex hull epigraph function. Furthermore, we develop cutting plane algorithm for constrained based on inequalities. Our computational experiments subproblem in robust coupled sensor placement show that our can solv...

In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtai...

INTRODUCTION In 2008, the Otoneurology committee of the SEORL-PCF published a classification of peripheral vertigo, based on clinical criteria. The objective of this study was to validate this classification through analysing the diagnostic agreement among several medical assessors. METHODS Seven medical assessors, all with clinical experience, from 6 different hospitals, participated in the ...