Abstract
In this paper a new weighted short-step primal-dual interior point algorithm to solve convex quadratic optimization (CQO) problems. The algorithm uses at each interior iteration afull-Newton step and the strategy of the central to obtain an epsilon-optimal solution of CQO. The algorithm yields the best currently best known theoretical complexity bound namely O(\sqrt(n) log n/epsilon).
Highlights
Consider the quadratic optimization (QO) problem in standard format: { }(P ) min cT x + 1 xT Qx : Ax = b, x ≥ 0 x and its dual problem (D) max bT y − 1 xT Qx : AT y + z − Qx = c, z ≥ 0, x, y, zISSN 2310-5070 ISSN 2311-004XCopyright ⃝c 2014 International Academic PressM
There are a variety of solution approaches for convex quadratic optimization (CQO) which have been studied intensively
Leads to the concept of Target-Following interior-point methods (IPMs) introduced by Jansen et al.,[6] as a generalization of the classical path-following methods
Summary
Consider the quadratic optimization (QO) problem in standard format:. (P ) min cT x + 1 xT Qx : Ax = b, x ≥ 0 x and its dual problem (D) max bT y − 1 xT Qx : AT y + z − Qx = c, z ≥ 0 , x, y, z. Feasible primal-dual path-following methods are the most attractive methods of IPMs [7, 9] Their derived algorithms achieved important results such as polynomial complexity and numerical efficiency. These algorithms trace approximately the so-called central-path which is a curve that lies in the feasible region of the considered problem and they reach an optimal solution of it. In practice these methods don’t always find a strictly feasible centered point to starting their derived algorithms. The vector of all ones and the identity matrix are denoted by e and I, respectively
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