We present in this paper the alternating minimization method on CAT(0) spaces for solving unconstraints convex optimization problems. Under the assumption that the function being minimize is convex, we prove that the sequence generated by our algorithm converges to a minimize point. The results presented in this paper are the first ones of this type that have been given for theses spaces and al...

the compressibility factor of nonassociated chain molecules composed of hard convex core yukawa segments was derived with saft-vr and an extension of the barker-henderson perturbation theory for convex bodies. the temperature-dependent chain and dispersion compressibility factors were derived using the yukawa potential. the effects of temperature, packing fraction, and segment number on the com...

reliability investigation has always been one of the most important issues in power systems planning. the outages rate in power system reflects the fact that more attentions should be paid on reliability indices to supply consumers with uninterrupted power. using reliability indices in economic dispatch problem may lead to the system load demand with high reliability and low probability of powe...

Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...

We develop and analyze a variant of Nesterov’s accelerated gradient descent (AGD) for minimization of smooth non-convex functions. We prove that one of two cases occurs: either our AGD variant converges quickly, as if the function was convex, or we produce a certificate that the function is “guilty” of being non-convex. This non-convexity certificate allows us to exploit negative curvature and ...

A quasiconvex function f being given, does there exist an increasing and continuous k which makes $$k\circ f$$ convex? How to build such a k? Some words on least convex (concave) functions. The ratio of two positive numbers is neither locally convexifiable nor concavifiable. Finally, some considerations the approximation preorder from finite number observations revealed preference problem are d...

We propose a novel asynchronous parallel algorithmic framework for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex constraints. The proposed framework hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of modern computational architectures and asynchro...

With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a numerical tool, based on recent ideas form non-convex optimization. The algorithm excels in the compressed-sensing-like situation, where only few data points are measured from a low-rank or highly-pure quantum ...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...