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Convex Optimization
A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency. Expand
Semidefinite Programming
A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given. Expand
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
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
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
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
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 constraints, yielding new results or new proofs for existing results from control theory. Expand
Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
It is shown that problem structure in the semidefinite programming formulation can be exploited to develop more efficient implementations of interior-point methods, and a variant of a simple subspace algorithm is presented in which low-rank matrix approximations are computed via nuclear norm minimization instead of the singular value decomposition. Expand
Interior-point methods
This work reviews some of the key developments in the modern era of interior-point methods, including comments on both the complexity theory and practical algorithms for linear programming, semide nite programming, monotone linear complementarity, and convex programming over sets that can be characterized by self-concordant barrier functions. Expand
Extended LMI characterizations for stability and performance of linear systems
A general, projection lemma based methodology for deriving extended LMI characterizations and a straightforward and unified proof for all known literature results as well as some currently missing extended LMIs are provided. Expand