# L. Vandenberghe

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- Publications
- Influence

Convex Optimization

- Stephen P. Boyd, L. Vandenberghe
- Computer Science, Mathematics
- IEEE Transactions on Automatic Control
- 1 March 2004

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 great… Expand

Semidefinite Programming

- L. Vandenberghe, Stephen P. Boyd
- Computer Science
- SIAM Rev.
- 1 March 1996

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 and… Expand

Applications of second-order cone programming

- M. Lobo, L. Vandenberghe, Stephen P. Boyd, Hervé Lebret
- Mathematics
- 15 November 1998

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 that… Expand

A tutorial on geometric programming

- Stephen P. Boyd, Seung-Jean Kim, L. Vandenberghe, A. Hassibi
- Mathematics
- 10 April 2007

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 can… Expand

Determinant Maximization with Linear Matrix Inequality Constraints

- L. Vandenberghe, Stephen P. Boyd, S. Wu
- Mathematics
- 1 April 1998

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

- H. Wolkowicz, R. Saigal, L. Vandenberghe
- Mathematics
- 2000

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 Semidefinite… Expand

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- PDF

Semidefinite programming duality and linear time-invariant systems

- V. Balakrishnan, L. Vandenberghe
- Computer Science, Mathematics
- IEEE Trans. Autom. Control.
- 22 January 2003

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

Interior-Point Method for Nuclear Norm Approximation with Application to System Identification

- Z. Liu, L. Vandenberghe
- Mathematics, Computer Science
- SIAM J. Matrix Anal. Appl.
- 1 August 2009

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 as… Expand

FIR Filter Design via Spectral Factorization and Convex Optimization

- S. Wu, Stephen P. Boyd, L. Vandenberghe
- Computer Science
- 1999

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 filter… Expand

Extended LMI characterizations for stability and performance of linear systems

- G. Pipeleers, B. Demeulenaere, J. Swevers, L. Vandenberghe
- Mathematics, Computer Science
- Syst. Control. Lett.
- 1 July 2009

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 for… Expand