This is the second part of a work devoted to the theory of epigraphical cones and their applications. A convex cone K in the Euclidean space Rn+1 is an epigraphical cone if it can be represented as epigraph of a nonnegative sublinear function f : Rn → R. We explore the link between the geometric properties of K and the analytic properties of f . Mathematics Subject Classification: 46B10, 46B20,...

Shohada (Sepah) avenue in Qazvin, a historic city, is a part of Safavid era infrastructure of the city. It connects various important cites and poles like Jame' mosque, Imamzadeh Hosein, Dowlat-Khaneh and the Traditional Bazaar complex to one another. This axis in KhomarTashi, in Kabir Jame' mosque - preservation and restoration of Jame' mosque complex as principle core of the city which is ...

We discuss two approaches to duality for multiple objective linear problems. The first approach is based on a duality relation between a set and its complement in the outcome space. It allows us to obtain a number of known duality constructions. The second approach utilizes polarity between a polyhedral set and the epigraph of its support function. It leads to a parametric dual problem which is...

We show that a locally Lipschitz homeomorphism function is semismooth at a given point if and only if its inverse function is semismooth at its image point. We present a sufficient condition for the semismoothness of solutions to generalized equations over cone reducible (nonpolyhedral) convex sets. We prove that the semismoothness of solutions to the Moreau-Yosida regularization of a lower sem...

We propose a method for zeroth order stochastic convex optimization that attains the suboptimality rate of Õ(n7T−1/2) after T queries for a convex bounded function f : R → R. The method is based on a random walk (the Ball Walk) on the epigraph of the function. The randomized approach circumvents the problem of gradient estimation, and appears to be less sensitive to noisy function evaluations c...

In sum, Experiment and interpretation is disappointing, both as a philosophical and a historical inquiry into the practice of science. It also stands as a poor memoir for a pathologist's lifelong investment in trying to understand experimentally the genesis of cancer-Salaman died just before the publication of this book. It certainly does not allow us, the readers, to understand the epigraph: f...

Let  R be bounded, open and convex. Let F W R ! R be convex, coercive of order p > 1 and such that the diameters of the projections of the faces of the epigraph of F are uniformly bounded. Then every minimizer of Z  F.rv.x// dx; v 2 CW 1;1 0 .;R/; is Hölder continuous in of order p 1 nCp 1 whenever is Lipschitz on @. A similar result for non convex Lagrangians that admit a minimizer follows.

In this paper we use the tools of the convex analysis in order to give a suitable characterization for the epigraph of the conjugate of the pointwise maximum of two proper, convex and lower semicontinuous functions in a normed space. By using this characterization we obtain, as a natural consequence, the formula for the biconjugate of the pointwise maximum of two functions, provided the so-call...

This paper deals with a class of stochastic optimal control problems (SOCP) in presence of state-constraints. It is well-known that for such problems the value function is, in general, discontinuous and its characterization by a Hamilton-Jacobi equation requires additional assumptions involving an interplay between the boundary of the set of constraints and the dynamics of the controlled system...