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semidefinite relaxation aided noncoherent detection in two-way relay transmission

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Frontiers of Information Technology & Electronic Engineering 2019年第9期20卷 1259-1265页

作者： Chan-fei WANG Ji-ai HE Wei-fang WANG Ya-mei XU School of Computer and Communication Lanzhou University of TechnologyLanzhou 730050China

A high-performance noncoherent transmission scheme is proposed in the broadcasting phase of a twoway relay transmission(TWRT),where multiple-symbol differential detection(MSDD)is performed because of its excellent detection performance with no channel ***,the generalized likelihood ratio test aided MSDD(GLRT-MSDD)is developed for the ***,GLRT-MSDD is reformulated and a semidefinite relaxation aided MSDD(SDR-MSDD)is *** reformulation of GLRT-MSDD to SDR-MSDD is desirable owing to its reduced *** analysis and the simulations validate that the proposed SDR-MSDD provides the bit-error-rate performance close to that of GLRT-MSDD with reasonable complexity in TWRT.

关键词： Multiple-symbol differential detection Generalized likelihood ratio test semidefinite relaxation Two-way relay transmission

A LOGARITHMIC BARRIER NEWTON METHOD FOR semidefinite PROGRAMMING

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Systems Science and Mathematical Sciences 1997年第2期10卷 168-175页

作者： JIANG Jianmin SHI Miaogen (Department of Applied Mathematics, Tsinghua University, Beijing 100084, China) 清华大学应用数学系北京

In this paper, by analyzing the properties of the central path, we give a logarithmic barrier Newton algorithm for semidefinite programming. It can be seen as an extension of the method for LP problems developed by Ro... 详细信息

关键词： semidefinite programming logarithmic barrier function central path projected Newton method.

CHARACTERISTIC FINITE DIFFERENCE METHODS FOR POSITIVE semidefinite PROBLEM OF TWO-PHASE(OIL AND WATER)MISCIBLE FLOW IN POROUS MEDIA

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Systems Science and Mathematical Sciences 1999年第4期12卷 299-306页

作者： YUAN Yirang(Institute of Mathematics, Shandong University, Jinan 250100, China)

Numerical simulation of two-phase (oil and water) miscible flow in porousmedia is the mathematical foundation in energy problems. For a two-dimensional posi-tive problem, Douglas put forward the well-known characteristic finite difference ***, for numerical analysis there exist difficulties. They assumed that the problem isperiodic and the diffusion matrix of the concentration equation was positive definite. Butin many practical situations the diffusion matrixes are only positive semidefinite. In thispaper, we put forward a kind of characteristic finite difference schemes and obtain optimalorder estimates in l2 norm for the error in the approximation assumptions.

关键词： Oil and water displacement miscible flow positive semidefinite characteristic finite difference 12 error estimate.

Safe Bounds in semidefinite Programming by Using Interval Arithmetic

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American Journal of Operations Research 2014年第5期4卷 293-300页

作者： Orkia Derkaoui Ahmed Lehireche Computer Science Department University Dr Moulay Tahar of Saida Saida Algeria Computer Science Department University Djillali Liabes of SidiBel Abbes SidiBel Abbes Algeria

Efficient solvers for optimization problems are based on linear and semidefinite relaxations that use floating point arithmetic. However, due to the rounding errors, relaxation thus may overestimate, or worst, underestimate the very global optima. The purpose of this article is to introduce an efficient and safe procedure to rigorously bound the global optima of semidefinite program. This work shows how, using interval arithmetic, rigorous error bounds for the optimal value can be computed by carefully post processing the output of a semidefinite programming solver. A lower bound is computed on a semidefinite relaxation of the constraint system and the objective function. Numerical results are presented using the SDPA (semidefinite Programming Algorithm), solver to compute the solution of semidefinite programs. This rigorous bound is injected in a branch and bound algorithm to solve the optimisation problem.

关键词： semidefinite Programming Interval Arithmetic Rigorous Error Bounds SDPA Solver Branch and Bound Algorithm

Some Properties of Solution to semidefinite Complementarity Problem

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Journal of Applied Mathematics and Physics 2018年第1期6卷 122-129页

作者： Yu Chen Cuiling Chen Caihong Han College of Mathematics and Statistics Guangxi Normal University Guilin China

In this paper, we discuss the nonemptyness and boundedness of the solution set for P*-semidefinite complementarity problem by using the concept of exceptional family of elements for complementarity problems over the cone of semidefinite matrices, and obtain a main result that if the corresponding problem has a strict feasible point, then its solution set is nonemptyness and boundedness.

关键词： semidefinite Complementarity Problem P*-Mapping Nonemptyness Boundedness

Optimization of a robust collaborative-relay beamforming design for simultaneous wireless information and power transfer

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Frontiers of Information Technology & Electronic Engineering 2018年第11期19卷 1432-1443页

作者： Lu-lu ZHAO Xing-long JIANG Li-min LI Guo-qiang ZENG Hui-jie LIU Shanghai Institute of Microsystem and Information Technology Chinese Academy of SciencesShanghai 200050China Shanghai Engineering Center for Microsatellites Shanghai 201210China College of Mathematics Physics and Electronic Information EngineeringWenzhou UniversityWenzhou 325035China

We investigate a collaborative-relay beamforming design for simultaneous wireless information and power transfer. A non-robust beamforming design that assumes availability of perfect channel state information(CSI) in the relay nodes is addressed. In practical scenarios, CSI errors are usually inevitable; therefore, a robust collaborativerelay beamforming design is proposed. By applying the bisection method and the semidefinite relaxation(SDR)technique, the non-convex optimization problems of both non-robust and robust beamforming designs can be ***, the solution returned by the SDR technique may not always be rank-one; thus, an iterative sub-gradient method is presented to acquire the rank-one solution. Simulation results show that under an imperfect CSI case, the proposed robust beamforming design can obtain a better performance than the non-robust one.

关键词： Simultaneous wireless information and power transfer Channel state information Robust beamforming semidefinite relaxation Iterative sub-gradient

Approximation algorithms for indefinite complex quadratic maximization problems

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Science China Mathematics 2010年第10期53卷 2697-2708页

作者： HUANG Yongwei1,& ZHANG Shuzhong2 1Department of Electronic and Computer Engineering,The Hong Kong University of Science and Technology,Kowloon,Hong Kong,China 2Department of Systems Engineering and Engineering Management,The Chinese University of Hong Kong,Shatin,Hong Kong,China 1. Department of Electronic and Computer Engineering The Hong Kong University of Science and Technology Kowloon Hong Kong China2. Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong Shatin Hong Kong China

In this paper,we consider the following indefinite complex quadratic maximization problem: maximize zHQz,subject to zk ∈ C and zkm = 1,k = 1,...,n,where Q is a Hermitian matrix with trQ = 0,z ∈ Cn is the decision vector,and m *** (1/log n) approximation algorithm is presented for such ***,we consider the above problem where the objective matrix Q is in bilinear form,in which case a 0.7118 cos mπ 2approximation algorithm can be *** the context of quadratic optimization,various extensions and connections of the model are discussed.

关键词： indefinite Hermitian matrix randomized algorithms approximation ratio semidefinite programming relaxation

A Modified Full-NT-Step Infeasible Interior-Point Algorithm for SDP Based on a Specific Kernel Function

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Journal of Harbin Institute of Technology(New Series) 2019年第2期26卷 41-47页

作者： Yadan Wang Hongwei Liu Zexian Liu Department of Mathematics Xidian University School of Mathematics and Computer Science Hezhou University

This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.

关键词： semidefinite programming infeasible interior-point methods full Nesterov-Todd steps kernel functions polynomial complexity

Higher-Order Duality for Minimax Fractional Type Programming Involving Symmetric Matrices

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Applied Mathematics 2011年第11期2卷 1387-1392页

作者： Caiyun Jin Cao-Zong Cheng College of Applied Sciences Beijing University of Technology

Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )β vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )β vector-pseudoquasi-Type I.

关键词： Higher-Order (F α p d b φ )β Vector-Pseudoquasi-Type I Higher-Order Duality Minimax Fractional Type Programming Positive semidefinite Symmetric Matrix