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dc.description.abstractSDP relaxatin과 SOCP relaxation은 Nonconvex Quadratic Optimization Problem(QOP)의 근사 해를 찾는다. 일반적으로 SOCP relaxation은 SDP relaxation 보다 정확한 해를 구하지 못한다. 우리는 second order cone 조건을 이용하여 SOCP relaxation을 확장시켜 더 정확한 해를 구하는 방법을 제안하고 수치적 실험 결과를 나열하여 제안 된 본 방법의 이점을 보여준다. 본 방법은 특히 Banded QOP에 대해 매우 효과적이다;Nonconvex Quadratic Optimization Problems (QOPs) are solved approximately by SDP(semidefinite programming) relaxation and SOCP (second-order-cone program) relaxation. We propose three methods to improved SOCP relaxation, each of which provides a way to find more accurate solutions. Numerical results are shown to illustrate advantages of the proposed methods.-
dc.description.tableofcontentsAbstract = ii Chapter 1 Introduction = 1 Chapter 2 Convexification = 4 2.1 Convex relaxation for the QOP = 4 2.2 Convex quadratic inequalities to obtain SOCP relaxation = 6 Chapter 3 An extension of the SOCP = 10 3.1 Basic Analysis = 10 3.2 The different types of SOCP = 11 3.3 An extension of SOCP for Banded system = 14 Chapter 4 Numerical results = 16 4.1 QOPs with banded Q_(p)'s = 17 4.2 QOPs with general Q_(p)'s = 19 Chapter 5 Concluding Discussions = 20 Bibliography = 21 논문초록-
dc.format.extent1668620 bytes-
dc.publisher이화여자대학교 대학원-
dc.titleAn extension of second order cone relaxation of a positive semidefinite constraint for banded systems-
dc.typeMaster's Thesis-
dc.format.pageii, 29 p-
dc.identifier.major대학원 수학과- 2-
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