Convex Optimization in Signal Processing and Communications最新文献

Robust broadband adaptive beamforming using convex optimization 基于凸优化的鲁棒宽带自适应波束形成

Convex Optimization in Signal Processing and Communications Pub Date : 2009-12-03 DOI: 10.1017/CBO9780511804458.010

M. Rübsamen, A. El-Keyi, A. Gershman, T. Kirubarajan

引用次数: 11

Semidefinite programming, matrix decomposition, and radar code design 半定规划，矩阵分解，和雷达代码设计

Convex Optimization in Signal Processing and Communications Pub Date : 1900-01-01 DOI: 10.1017/CBO9780511804458.007

Yongwei Huang, A. Maio, Shuzhong Zhang

{"title":"Semidefinite programming, matrix decomposition, and radar code design","authors":"Yongwei Huang, A. Maio, Shuzhong Zhang","doi":"10.1017/CBO9780511804458.007","DOIUrl":"https://doi.org/10.1017/CBO9780511804458.007","url":null,"abstract":"In this chapter, we study specific rank-1 decomposition techniques for Hermitian positive semidefinite matrices. Based on the semidefinite programming relaxation method and the decomposition techniques, we identify several classes of quadratically constrained quadratic programming problems that are polynomially solvable. Typically, such problems do not have too many constraints. As an example, we demonstrate how to apply the new techniques to solve an optimal code design problem arising from radar signal processing. Introduction and notation Semidefinite programming (SDP) is a relatively new subject of research in optimization. Its success has caused major excitement in the field. One is referred to Boyd and Vandenberghe [11] for an excellent introduction to SDP and its applications. In this chapter, we shall elaborate on a special application of SDP for solving quadratically constrained quadratic programming (QCQP) problems. The techniques we shall introduce are related to how a positive semidefinite matrix can be decomposed into a sum of rank-1 positive semidefinite matrices, in a specific way that helps to solve nonconvex quadratic optimization with quadratic constraints. The advantage of the method is that the convexity of the original quadratic optimization problem becomes irrelevant; only the number of constraints is important for the method to be effective. We further present a study on how this method helps to solve a radar code design problem. Through this investigation, we aim to make a case that solving nonconvex quadratic optimization by SDP is a viable approach.","PeriodicalId":358416,"journal":{"name":"Convex Optimization in Signal Processing and Communications","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114213203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 30

Cooperative distributed multi-agent optimization 协同分布式多智能体优化

Convex Optimization in Signal Processing and Communications Pub Date : 1900-01-01 DOI: 10.1017/CBO9780511804458.011

Angelia Nenadic, A. Ozdaglar

{"title":"Cooperative distributed multi-agent optimization","authors":"Angelia Nenadic, A. Ozdaglar","doi":"10.1017/CBO9780511804458.011","DOIUrl":"https://doi.org/10.1017/CBO9780511804458.011","url":null,"abstract":"This chapter presents distributed algorithms for cooperative optimization among multiple agents connected through a network. The goal is to optimize a global-objective function which is a combination of local-objective functions known by the agents only. We focus on two related approaches for the design of distributed algorithms for this problem. The first approach relies on using Lagrangian-decomposition and dual-subgradient methods. We show that this methodology leads to distributed algorithms for optimization problems with special structure. The second approach involves combining consensus algorithms with subgradient methods. In both approaches, our focus is on providing convergence-rate analysis for the generated solutions that highlight the dependence on problem parameters. Introduction and motivation There has been much recent interest in distributed control and coordination of networks consisting of multiple agents, where the goal is to collectively optimize a global objective. This is motivated mainly by the emergence of large-scale networks and new networking applications such as mobile ad hoc networks and wireless-sensor networks, characterized by the lack of centralized access to information and time-varying connectivity. Control and optimization algorithms deployed in such networks should be completely distributed, relying only on local observations and information, robust against unexpected changes in topology, such as link or node failures, and scalable in the size of the network. This chapter studies the problem of distributed optimization and control of multiagent networked systems. More formally, we consider a multiagent network model, where m agents exchange information over a connected network.","PeriodicalId":358416,"journal":{"name":"Convex Optimization in Signal Processing and Communications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128800086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 185

Nash equilibria: the variational approach 纳什均衡:变分方法

Convex Optimization in Signal Processing and Communications Pub Date : 1900-01-01 DOI: 10.1017/CBO9780511804458.013

F. Facchinei, J. Pang

引用次数: 155