A full NT-step O(n) infeasible interior-point method for Cartesian P_*(k) –HLCP over symmetric cones using exponential convexity

Document Type: research paper

Authors

1 Professor, Department of Applied Mathematics (Optimization), Azarbaijan Shahid Madani University, Tabriz, Iran

2 Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

Abstract

In this paper, by using the exponential convexity property of a barrier function, we propose an infeasible interior-point method for Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones. The method uses Nesterov and Todd full steps, and we prove that the proposed algorithm is well define. The iteration bound coincides with the currently best iteration bound for the Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones.

Keywords


Article Title [Persian]

یک روش نقطه درونی نشدنی با گام کامل NT با پیچیدگی (O(n برای حاصل‌ضرب دکارتی P_*(k) –HLCP روی مخروط‌های متقارن با استفاده از تحدب نمایی

Authors [Persian]

  • بهروز خیرفام 1
  • معصومه حقیقی 2
1 گروه ریاضی کاربردی (بهینه سازی)، دانشکده علوم پایه، دانشگاه شهید مدنی آذربایجان، تبریز، ایران
2 گروه ریاضی کاربردی (بهینه سازی)، دانشکده علوم پایه، دانشگاه شهید مدنی آذربایجان، تبریز، ایران
Abstract [Persian]

در این مقاله،  با استفاده از خاصیت تحدب نمایی یک تابع مانع، یک روش نقطه درونی نشدنی را برای مساله حاصل‌ضرب دکارتی مکملی خطی افقی روی مخروط‌های متقارن  ارایه می­دهیم. در این روش، از گام‌های کامل نسترو-تاد استفاده کرده و نشان می­دهیم که الگوریتم منظور شده خوش تعریف است. کران تکرار الگوریتم با بهترین کران تکرار شناخته شده برای مسایل حاصل‌ضرب دکارتی مکملی خطی افقی روی مخروط­های متقارن  منطبق است. هزینه اجرای یک تکرار  عملیات حسابی است.

Keywords [Persian]

  • مساله‌ مکملی خطی افقی
  • حاصل‌ضرب دکارتی
  • روش نقطه درونی نشدنی
  • پیچیدگی چندجمله‌ای
  • مخروط متقارن
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