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1Convex Relaxation for Optimal Distributed Control Problem
"... Abstract—This paper is concerned with the optimal distributed control (ODC) problem for discretetime deterministic and stochastic systems. The objective is to design a fixedorder distributed controller with a prespecified structure that is globally optimal with respect to a quadratic cost functi ..."
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functional. It is shown that this NPhard problem has a quadratic formulation, which can be relaxed to a semidefinite program (SDP). If the SDP relaxation has a rank1 solution, a globally optimal distributed controller can be recovered from this solution. By utilizing the notion of treewidth, it is proved
Convex relaxation for optimal distributed control problem—part II: Lyapunov formulation and case studies
 Online]. Available: http://www.ee.columbia.edu/lavaei/Dec Control 2014 PartII.pdf
, 2014
"... Abstract—This paper is concerned with the optimal distributed control (ODC) problem. The objective is to design a fixedorder distributed controller with a prespecified structure for a discretetime system. It is shown that this NPhard problem has a quadratic formulation, which can be relaxed to ..."
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Cited by 4 (4 self)
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Abstract—This paper is concerned with the optimal distributed control (ODC) problem. The objective is to design a fixedorder distributed controller with a prespecified structure for a discretetime system. It is shown that this NPhard problem has a quadratic formulation, which can be relaxed
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 496 (2 self)
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. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
Global Optimization with Polynomials and the Problem of Moments
 SIAM Journal on Optimization
, 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear mat ..."
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Cited by 569 (47 self)
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We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear
Optimization Flow Control, I: Basic Algorithm and Convergence
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1999
"... We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm. In thi ..."
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Cited by 690 (64 self)
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We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm
Constrained model predictive control: Stability and optimality
 AUTOMATICA
, 2000
"... Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence and t ..."
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Cited by 696 (15 self)
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Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence
A firstorder primaldual algorithm for convex problems with applications to imaging
, 2010
"... In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering in this paper ..."
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Cited by 435 (20 self)
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In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Distributed Database Systems
"... this article, we discuss the fundamentals of distributed DBMS technology. We address the data distribution and architectural design issues as well as the algorithms that need to be implemented to provide the basic DBMS functions such as query processing, concurrency control, reliability, and replica ..."
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Cited by 586 (26 self)
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this article, we discuss the fundamentals of distributed DBMS technology. We address the data distribution and architectural design issues as well as the algorithms that need to be implemented to provide the basic DBMS functions such as query processing, concurrency control, reliability
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