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Convex Optimization
Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with greatExpand
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Semidefinite Programming
In semidefinite programming, one minimizes a linear function subject to the constraint that an affine combination of symmetric matrices is positive semidefinite. Such a constraint is nonlinear andExpand
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Applications of second-order cone programming
In a second-Order cone program (SOCP) a linear function is minimized over the intersection of an affine set and the product of second-Order (quadratic) cones. SOCPs are nonlinear convex Problems thatExpand
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A tutorial on geometric programming
Abstract A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods canExpand
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Determinant Maximization with Linear Matrix Inequality Constraints
The problem of maximizing the determinant of a matrix subject to linear matrix inequalities (LMIs) arises in many fields, including computational geometry, statistics, system identification,Expand
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Handbook of semidefinite programming : theory, algorithms, and applications
Contributing Authors. List of Figures. List of Tables. Preface. 1. Introduction H. Wolkowicz, et al. Part I: Theory. 2. Convex Analysis on Symmetric Matrices F. Jarre. 3. The Geometry of SemidefiniteExpand
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Semidefinite programming duality and linear time-invariant systems
Several important problems in control theory can be reformulated as semidefinite programming problems, i.e., minimization of a linear objective subject to linear matrix inequality (LMI) constraints.Expand
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Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
The nuclear norm (sum of singular values) of a matrix is often used in convex heuristics for rank minimization problems in control, signal processing, and statistics. Such heuristics can be viewed asExpand
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FIR Filter Design via Spectral Factorization and Convex Optimization
We consider the design of finite impulse response (FIR) filters subject to upper and lower bounds on the frequency response magnitude. The associated optimization problems with the filterExpand
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Extended LMI characterizations for stability and performance of linear systems
Over the past ten years, extensive research has been devoted to extended LMI characterizations for stability and performance of linear systems. These characterizations constitute a valuable tool forExpand
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