A note on KKT points of homogeneous programs

Homogeneous programming is an important class of optimization problems. The purpose of this note is to give a truly equivalent characterization of KKT-points of homogeneous programming problems, which corrects a result given in [9]. Article Download View A note on KKT points of homogeneous programs

Constructing Generalized Mean Functions Using Convex Functions with Regularity Conditions

The generalized mean function has been widely used in convex analysis and mathematical programming. This paper studies a further generalization of such a function. A necessary and sufficient condition is obtained for the convexity of a generalized function. Additional sufficient conditions that can be easily checked are derived for the purpose of identifying some classes … Read more

A predictor-corrector algorithm for linear optimization based on a specific self-regular proximity function

It is well known that the so-called first-order predictor-corrector methods working in a large neighborhood of the central path are among the most efficient interior-point methods (IPMs) for linear optimization (LO) problems. However, the best known iteration complexity of this type of methods is $O\br{n \log\frac{(x^0)^Ts^0}{\varepsilon}}$. It is of interests to investigate whether the complexity … Read more

A new path-following algorithm for nonlinear P_* complementarity problems

Inspired by the recent theoretical results of Zhao and Li [{\em Math. Oper. Res.,} 26 (2001), pp. 119-146], we present in this paper a new path-following method for nonlinear P$_*$ complementarity problems. Different from most existing interior-point algorithms that are based on the central path, this algorithm is to track the newly defined “regularized central … Read more