We perform an average analysis of the Grassmann condition number C (A) for the homogeneous convex feasibility problem ∃x ∈ C \ 0 : Ax = 0, where C ⊂ R may be any regular cone. This in particular includes the cases of linear programming, second-order programming, and semidefinite programming. We thus give the first average analysis of convex programming, which is not restricted to linear program...

Problems of finding an arbitrary point of convex feasible set (convex feasibility problem, CFP), stationary points of monotone mappings (convex optimization, variational inequalities) are quite common objects of investigation in theory and applications [1]. One of the unifying themes for algorithmic developments in these areas are Fejer processes [2] which serve as a convenient abstraction to s...

The classical convex feasibility problem in a finite dimensional Euclidean space consists of finding point the intersection two sets. In present paper we are interested particular instances this problem. First, assume to know how compute an exact projection onto one sets involved and other set is compact such that conditional gradient (CondG) method can be used for computing efficiently inexact...

Abstract In this paper, we introduce a regularization method for solving the variational inclusion problem of sum two monotone operators in real Hilbert spaces. We suggest and analyze under some mild appropriate conditions imposed on parameters, which allow us to obtain short proof another strong convergence theorem problem. also apply our main result fixed point nonexpansive inequality problem...

Abstract In this paper our interest is in investigating properties and numerical solutions of Proximal Split feasibility Problems. First, we consider the problem of finding a point which minimizes a convex function f such that its image under a bounded linear operator A minimizes another convex function g. Based on an idea introduced in [9], we propose a split proximal algorithm with a way of s...

A novel unified approach to jointly optimize structural design parameters, actuator and sensor precision, controller parameters is presented in this paper. The joint optimization problem posed as a covariance control problem, where feasibility achieved by bounding the of output well that signals. formulation used tensegrity system, initial prestress precisions, law are optimized. Tensegrity sys...

In this paper, we implement Zhang’s method [22], which transforms a general convex optimization problem with smooth convex constraints into a convex conic optimization problem and then apply the techniques of self-dual embedding and central path following for solving the resulting conic optimization model. A crucial advantage of the approach is that no initial solution is required, and the meth...

We introduce the online stochastic Convex Programming (CP) problem, a very general version of stochastic online problems which allows arbitrary concave objectives and convex feasibility constraints. Many wellstudied problems like online stochastic packing and covering, online stochastic matching with concave returns, etc. form a special case of online stochastic CP. We present fast algorithms f...