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Error Bounds for Eigenvalue and Semidefinite Matrix Inequality Systems
"... Dedicated to Terry Rockafellar in honor of his 70th birthday Received: date / Revised version: date Abstract. In this paper we give sufficient conditions for existence of error bounds for systems expressed in terms of eigenvalue functions (such as in eigenvalue optimization) or positive semidefinite ..."
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Cited by 2 (0 self)
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Dedicated to Terry Rockafellar in honor of his 70th birthday Received: date / Revised version: date Abstract. In this paper we give sufficient conditions for existence of error bounds for systems expressed in terms of eigenvalue functions (such as in eigenvalue optimization) or positive
An InteriorPoint Method for Semidefinite Programming
, 2005
"... We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as maxcut. Other appli ..."
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Cited by 254 (19 self)
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We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as maxcut. Other
DETERMINANT MAXIMIZATION WITH LINEAR MATRIX INEQUALITY CONSTRAINTS
"... The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the s ..."
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Cited by 223 (18 self)
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The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization
A Rank Minimization Heuristic with Application to Minimum Order System Approximation
, 2001
"... Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) constraints. Except in some special cases, solving this rank minimization probiem (globally) is ve ..."
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Cited by 274 (10 self)
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Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) constraints. Except in some special cases, solving this rank minimization probiem (globally
PrimalDual PathFollowing Algorithms for Semidefinite Programming
 SIAM Journal on Optimization
, 1996
"... This paper deals with a class of primaldual interiorpoint algorithms for semidefinite programming (SDP) which was recently introduced by Kojima, Shindoh and Hara [11]. These authors proposed a family of primaldual search directions that generalizes the one used in algorithms for linear programmin ..."
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Cited by 165 (12 self)
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This paper deals with a class of primaldual interiorpoint algorithms for semidefinite programming (SDP) which was recently introduced by Kojima, Shindoh and Hara [11]. These authors proposed a family of primaldual search directions that generalizes the one used in algorithms for linear
Polynomial Matrix Inequality and Semidefinite Representation
, 908
"... Consider a convex set S = {x ∈ D: G(x) ≽ 0} where G(x) is an m × m symmetric matrix whose every entry is a polynomial or rational function, D ⊆ R n is a domain where G(x) is defined, and G(x) ≽ 0 means G(x) is positive semidefinite. The set S is called semidefinite programming (SDP) representable ..."
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Cited by 3 (1 self)
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or just semidefinite representable if it equals the projection of a higher dimensional set which is defined by a linear matrix inequality (LMI). This paper studies sufficient conditions guaranteeing semidefinite representability of S. We prove that S is semidefinite representable in the following cases
Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems
 IEEE Transactions on Automatic Control
, 1998
"... . This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. The relation to frequency domain methods such as the cir ..."
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Cited by 259 (4 self)
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. This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. The relation to frequency domain methods
Applications of Semidefinite Programming
, 1998
"... A wide variety of nonlinear convex optimization problems can be cast as problems involving linear matrix inequalities (LMIs), and hence efficiently solved using recently developed interiorpoint methods. In this paper, we will consider two classes of optimization problems with LMI constraints: ffl ..."
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Cited by 10 (0 self)
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The semidefinite programming problem, i.e., the problem of minimizing a linear function subject to a linear matrix inequality. Semidefinite programming is an important numerical tool for analysis and synthesis in systems and control theory. It has also been recognized in combinatorial optimization as a valuable
A Linear Matrix Inequality Approach to H∞ Control
 INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
, 1994
"... The continuous and discretetime H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMIbased parametrization of all H ..."
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Cited by 169 (11 self)
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The continuous and discretetime H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMIbased parametrization of all
A Newtonlike Method for Nonlinear Semidefinite Inequalities
"... A matrix map F (x) is said to be (matricially) convex, if u T F (x)u is a convex function for every u. In this paper, semidefinite systems of the type F (x) ¯ 0, where F (x) is matricially convex, are considered. This class of problems generalizes both affine semidefinite inequalities as well as o ..."
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A matrix map F (x) is said to be (matricially) convex, if u T F (x)u is a convex function for every u. In this paper, semidefinite systems of the type F (x) ¯ 0, where F (x) is matricially convex, are considered. This class of problems generalizes both affine semidefinite inequalities as well
Results 1  10
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2,196