The paper clarifies the literary function of Shevchenko’s “Jeremiah’s prayer”. At same time, it raises question poet’s identification and self-identification with Prophet Jeremiah because these issues can only be addressed in conjunction. Based on findings many researchers prayer” discussion between Shchurat Franko 1904 about Shevchenko Jeremiah, author concludes that is an epigraph not a rough...

In this paper, we proposed an alternating projection based algorithm to solve a class of distributed MIN-MAX convex optimization problems. We firstly transform this MINMAX problem into the problem of searching for the minimum distance between some hyper-plane and the intersection of the epigraphs of convex functions. The Bregmans alternating method is employed in our algorithm to achieve the di...

We consider the DC (difference of two convex functions) optimization problem ðPÞ inf x∈Xfðf 1ðxÞ− f 2ðxÞÞ þ ðg1ðAxÞ− g2ðAxÞÞg, where f 1, f 2, g1, and g2 are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y , and A is a linear continuous operator from X to Y . Adopting different tactics, two types of the Fenchel dual problems of ðPÞ are given. By usi...

The proper management of wireless mesh network is a challenging task due to the mobility of node and velocity of node. All devices work in open channel area due to this security is very challenging task. Because due to mobility and open channel area possibility of threats and attacks are very high. On the basis of related work we found data wormhole attack is a serious attack in the environment...

Nowadays, solving nonsmooth (not necessarily differentiable) optimization problems plays a very important role in many areas of industrial applications. Most of the algorithms developed so far deal only with nonsmooth convex functions. In this paper, we propose a new algorithm for solving nonsmooth optimization problems that are not assumed to be convex. The algorithm combines the traditional c...

Modern life sciences are becoming increasingly data intensive, posing a significant challenge for most researchers and shifting the bottleneck of scientific discovery from data generation to data analysis. As a result, progress in genome research is increasingly impeded by bioinformatic hurdles. A new generation of powerful and easy-to-use genome analysis tools has been developed to address thi...

Abstract In this paper, we study the convex quadratic optimization problem with indicator variables. For $${2\times 2}$$ 2 × case, describe hull of epigraph in original space variables, and also give a conic extended formulation. Then, using description for case as buil...

Quadratically constrained quadratic programs (QCQPs) are a fundamental class of optimization problems well-known to be NP-hard in general. In this paper we study conditions under which the standard semidefinite program (SDP) relaxation QCQP is tight. We begin by outlining general framework for proving such sufficient conditions. Then using framework, show that SDP tight whenever eigenvalue mult...

In both pure and applied mathematics, convex functions are used in many different problems. They crucial to investigate linear non-linear programming issues. Since a function is one whose epigraph set, the theory of falls under umbrella convexity. However, it significant that affects practically all areas mathematics. this paper, we introduce notions g,h-convexity or convexity with respect pair...