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S. Boyd

Bio: S. Boyd is an academic researcher. The author has contributed to research in topics: Control theory. The author has an hindex of 1, co-authored 1 publications receiving 11153 citations.

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Book
01 Nov 2008
TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
Abstract: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

17,420 citations

Book
26 Jun 2003
TL;DR: Preface, Notations 1.Introduction to Time-Delay Systems I.Robust Stability Analysis II.Input-output stability A.LMI and Quadratic Integral Inequalities Bibliography Index
Abstract: Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

4,200 citations

Journal ArticleDOI
01 Mar 1996
TL;DR: A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given.
Abstract: 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 nonsmooth, but convex, so semidefinite programs are convex optimization problems. Semidefinite programming unifies several standard problems (e.g., linear and quadratic programming) and finds many applications in engineering and combinatorial optimization. Although semidefinite programs are much more general than linear programs, they are not much harder to solve. Most interior-point methods for linear programming have been generalized to semidefinite programs. As in linear programming, these methods have polynomial worst-case complexity and perform very well in practice. This paper gives a survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution.

3,949 citations

Journal ArticleDOI
TL;DR: This algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.
Abstract: We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2-satisfiability (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 to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of 1/2 for MAX CUT and 3/4 or MAX 2SAT. Slight extensions of our analysis lead to a.79607-approximation algorithm for the maximum directed cut problem (MAX DICUT) and a.758-approximation algorithm for MAX SAT, where the best previously known approximation algorithms had performance guarantees of 1/4 and 3/4, respectively. Our algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.

3,932 citations

Book
05 Oct 1997
TL;DR: In this article, the authors introduce linear algebraic Riccati Equations and linear systems with Ha spaces and balance model reduction, and Ha Loop Shaping, and Controller Reduction.
Abstract: 1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

3,471 citations