AN INTERIOR-POINT ALGORITHM FOR SIMPLICIAL CONE CONSTRAINED CONVEX QUADRATIC OPTIMIZATION

Abstract

In this paper, we are concerned with the numerical solution of simplicial cone constrained convex quadratic optimization (SCQO) problems. A reformulation of the K.K.T optimality conditions of SCQOs as an equivalent linear complementarity problem with $\mathcal{P}$-matrix ($\mathcal{P}$-LCP) is considered. Then, a feasible full-Newton step interior-point algorithm (IPA) is applied for solving SCQO via $\mathcal{P}$-LCP. For the completeness of the study, we prove that the proposed algorithm is well-defined and converges locally quadratic to an optimal of SCQOs. Moreover, we obtain the currently best well-known iteration bound for the algorithm with short-update method, namely,$ \mathcal{O}(\sqrt{n}\log\frac{n}{\epsilon })$. Finally, we present a various set of numerical results to show its efficiency.