سامانه پژوهشی دانشگاه شهید مدنی آذربایجان | Polynomial convergence of two higher order interior-point methods for P∗(κ)-LCP in a wide neighborhood of the central path

عنوان	Polynomial convergence of two higher order interior-point methods for P∗(κ)-LCP in a wide neighborhood of the central path
نوع پژوهش	مقاله چاپ شده
کلیدواژه‌ها	Keywords Linear complementarity problem · Interior-point methods · Corrector–predictor methods · Superlinear convergence · Wide neighborhood · Polynomial complexity
چکیده	Abstract In this paper, we propose two interior-point methods for solving P∗(κ)-linear complementarity problems (P∗(κ)-LCPs): a high order large update path following method and a high order corrector–predictor method. Both algorithms generate sequences of iterates in the wide neighborhood (N−2,τ (α)) of the central path introduced by Ai and Zhang. The methods do not depend on the handicap κ of the problem so that they work for any P∗(κ)- LCP . They have O((1+κ)√nL) iteration complexity, the best-known iteration complexity obtained so far by any interior-point method for solving P∗(κ)-LCP. The high order corrector– predictor algorithm is superlinearly convergent with Q-order (mp+1) for problems that admit a strict complementarity solution and (mp+1)/2 for general problems, wheremp is the order of the predictor step.
پژوهشگران	بهروز خیرفام (نفر اول)، مریم چیت ساز (نفر دوم)

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