A Weighted Target- following Algorithm for Linearly Constrained Convex Optimization

Abstract

In recent years, convex optimization solved very large practical engineering problems reliably and eciently. In this paper, we present an extension of an algorithm for convex quadratic programming using a new technique for nding a class of search directions and the strategy of the central path, for convex optimization under linear constraints. To solve the initialization problem, we have introduced a weighted vector with the property that starting from an initial feasible centred point, it generates iterates that simultaneously, gets closer to optimality and closer to centrality. Finally, the favorable polynomial complexity bound for the algorithm is deserved namely, O ( p n log( x t z )) iterations.