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32
A Newtonlike method for solving rank constrained linear matrix inequalities
 in Proc. 43rd IEEE Conference on Decision and Control
, 2004
"... Abstract — This paper presents a Newton–like algorithm for solving systems of rank constrained linear matrix inequalities. Though local quadratic convergence of the algorithm is not a priori guaranteed or observed in all cases, numerical experiments, including application to an output feedback stabi ..."
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Cited by 30 (4 self)
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Abstract — This paper presents a Newton–like algorithm for solving systems of rank constrained linear matrix inequalities. Though local quadratic convergence of the algorithm is not a priori guaranteed or observed in all cases, numerical experiments, including application to an output feedback stabilization problem, show the effectiveness of the algorithm. I.
Controller design via nonsmooth multidirectional search
 SIAM J. Control Optim
, 2006
"... z Abstract We propose an algorithm which combines multidirectional search (MDS) with nonsmooth optimization techniques to solve difficult problems in automatic control. Applications include static and fixedorder output feedback controller design, simultaneous stabilization, H2=H1 synthesis and muc ..."
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Cited by 23 (13 self)
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z Abstract We propose an algorithm which combines multidirectional search (MDS) with nonsmooth optimization techniques to solve difficult problems in automatic control. Applications include static and fixedorder output feedback controller design, simultaneous stabilization, H2=H1 synthesis and much else. We show how to combine direct search techniques with nonsmooth descent steps in order to obtain convergence certificates in the presence of nonsmoothness. Our technique is the most efficient when small controllers for plants with large state dimension are sought. Our numerical testing includes several benchmark examples. For instance, our algorithm needs 0.41 seconds to compute a static output feedback stabilizing controller for the Boeing 767 flutter benchmark problem [22], a system with 55 states. The first static controller without performance specifications for this system was obtained in [16]. Keywords: N Phard design problems, static output feedback, fixedorder synthesis, simultaneous stabilization, mixed H2=H1synthesis, pattern search algorithm, moving polytope, nonsmooth analysis, spectral bundle method, "gradients, bilinear matrix inequality (BMI).
Partially augmented Lagrangian method for matrix inequalities
 SIAM J. on Optimization
"... Pierre Apkarian k Abstract We discuss a partially augmented Lagrangian method for optimization programs with matrix inequality constraints. A global convergence result is obtained. Applications to hard problems in feedback control are presented to validate the method numerically. ..."
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Cited by 17 (7 self)
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Pierre Apkarian k Abstract We discuss a partially augmented Lagrangian method for optimization programs with matrix inequality constraints. A global convergence result is obtained. Applications to hard problems in feedback control are presented to validate the method numerically.
A spectral quadraticSDP method with applications to fixedorder H2 and H∞ synthesis
"... In this paper, we discuss a spectral quadraticSDP method for the iterative resolution of fixedorder H2 and H∞ design problems. These problems can be cast as regular SDP programs with additional nonlinear equality constraints. When the inequalities are absorbed into a Lagrangian function the probl ..."
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Cited by 13 (7 self)
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In this paper, we discuss a spectral quadraticSDP method for the iterative resolution of fixedorder H2 and H∞ design problems. These problems can be cast as regular SDP programs with additional nonlinear equality constraints. When the inequalities are absorbed into a Lagrangian function the problem reduces to solving a sequence of SDPs with quadratic objective function for which a spectral SDP method has been developed. Besides a description of the spectral SDP method used to solve the tangent subproblems, we report a number of computational results for validation purposes.
Nonlinear spectral SDP method for BMIconstrained problems: Applications to control design
 in Proceedings ICINCO
, 2004
"... Bilinear matrix inequality, spectral penalty function, trustregion, control synthesis. The purpose of this paper is to examine a nonlinear spectral semidefinite programming method to solve problems with bilinear matrix inequality (BMI) constraints. Such optimization programs arise frequently in aut ..."
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Cited by 12 (10 self)
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Bilinear matrix inequality, spectral penalty function, trustregion, control synthesis. The purpose of this paper is to examine a nonlinear spectral semidefinite programming method to solve problems with bilinear matrix inequality (BMI) constraints. Such optimization programs arise frequently in automatic control and are difficult to solve due to the inherent nonconvexity. The method we discuss here is of augmented Lagrangian type and uses a succession of unconstrained subproblems to approximate the BMI optimization program. These tangent programs are solved by a trust region strategy. The method is tested against several difficult examples in feedback control synthesis. 1
A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems
 SIAM J. OPTIM
, 2004
"... We study a smoothing Newton method for solving a nonsmooth matrix equation that includes semidefinite programming and the semidefinite complementarity problem as special cases. This method, if specialized for solving semidefinite programs, needs to solve only one linear system per iteration and achi ..."
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Cited by 12 (5 self)
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We study a smoothing Newton method for solving a nonsmooth matrix equation that includes semidefinite programming and the semidefinite complementarity problem as special cases. This method, if specialized for solving semidefinite programs, needs to solve only one linear system per iteration and achieves quadratic convergence under strict complementarity and nondegeneracy. We also establish quadratic convergence of this method applied to the semidefinite complementarity problem under the assumption that the Jacobian of the problem is positive definite on the affine hull of the critical cone at the solution. These results are based on the strong semismoothness and complete characterization of the Bsubdifferential of a corresponding squared smoothing matrix function, which are of general theoretical interest.
Trust region spectral bundle method for nonconvex eigenvalue optimization
, 2008
"... We present a nonsmooth optimization technique for nonconvex maximum eigenvalue functions and for nonsmooth functions which are infinite maxima of eigenvalue functions. We prove global convergence of our method in the sense that for an arbitrary starting point, every accumulation point of the sequen ..."
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Cited by 11 (8 self)
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We present a nonsmooth optimization technique for nonconvex maximum eigenvalue functions and for nonsmooth functions which are infinite maxima of eigenvalue functions. We prove global convergence of our method in the sense that for an arbitrary starting point, every accumulation point of the sequence of iterates is critical. The method is tested on several problems in feedback control synthesis.
MIXED H2/H∞ CONTROL VIA NONSMOOTH OPTIMIZATION
, 2008
"... We present a new approach to mixed H2/H∞ output feedback control synthesis. Our method uses nonsmooth mathematical programming techniques to compute locally optimal H2/H∞controllers, which may have a predefined structure. We prove global convergence of our method and present tests to validate it nu ..."
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Cited by 11 (7 self)
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We present a new approach to mixed H2/H∞ output feedback control synthesis. Our method uses nonsmooth mathematical programming techniques to compute locally optimal H2/H∞controllers, which may have a predefined structure. We prove global convergence of our method and present tests to validate it numerically.
A masked spectral bound for maximumentropy sampling
 In: mODa 7–Advances in ModelOriented Design and Analysis, Contributions to Statistics
, 2004
"... LIMITED DISTRIBUTION NOTICE: This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its ..."
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Cited by 7 (1 self)
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LIMITED DISTRIBUTION NOTICE: This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). Copies may be requested from IBM T. J. Watson Research