In this paper, we define a class of linear conic programming (which we call matrix cone programming or MCP) involving the epigraphs of five commonly used matrix norms and the well studied symmetric cone. MCP has recently found many important applications, for example, in nuclear norm relaxations of affine rank minimization problems. In order to make the defined MCP tractable and meaningful, we ...

in the architecture of iranian traditional houses, the ornamentations available in the inscriptions of houses entrance portal express the identity of architects and personality of houses owners and are rooted in their religious and national beliefs and faiths. the main hypothesis of this research is changing the physique and application of religious contents in compliance with the thoughts and ...

In this brief paper, we focus on the monument of C. Memmius and its inscription in Ephesus western Turkey. was grandson Sulla mentioned Ephesian as epigraph dedicatee. After discussing monument’s function, dating from different perspectives, concluding part, refer to positive memory Asia Minor, especially Ephesus.

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 ci...

Let g be a continuously differentiable function whose derivative is matrix monotone on positive semi-axis. Such a function induces a function φ(x) = tr(g(x)) on the cone of squares of an arbitrary Euclidean Jordan algebra. We show that φ(x)− ln det(x) is a self-concordant function on the interior of the cone. We also show that − ln(t−φ(x))−ln det(x) is √ 5 3 (r+1)-self-concordant barrier on the...

1.1 Definitions We say a set S ⊆ Rd is convex if for any two points x,x′ ∈ S, the line segment conv{x,x′} := {(1−α)x+αx′ : α ∈ [0, 1]} between x and x′ (also called the convex hull of {x,x′}) is contained in S. Overloading terms, we say a function f : S → R is convex if its epigraph epi(f) := {(x, t) ∈ S × R : f(x) ≤ t} is a convex set (in Rd × R). Proposition 1. A function f : S → R is convex ...

We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is weaker than all existing constraint qualifications, including the closed epigraph condition. Our dual condition was inspired by, and is weaker than, the so-called Bertsekas’ condition for monotropic programming problems. We give several corollaries of...

A method from a class of bundle methods is proposed to solve an unconstrained optimization problem. In this method an epigraph of the objective function is approximated by the set which is formed on the basis of the convex quadratic function. This method is characterized in that iteration points are constructed in terms of information obtained in the previous steps of the minimization process. ...

Epigenetic marks, such as DNA methylation and histone modifications, are important regulatory mechanisms that allow a single genomic sequence to give rise to a complex multicellular organism. When studying mechanisms of epigenetic regulation, the analyses depend on the experimental technologies and the available data. Recent advancements in sequencing technologies allow for the efficient extrac...