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Receding Horizon Control of Nonlinear Systems: A Control . . .
, 2000
"... n Automatic Control, pages 898 907, 1990. J. Shamma and M. Athans. Guaranteed properties of gain scheduled control for linear parametervarying plants. Automatica, pages 559 564, 1991. J. Shamma and M. Athans. Gainscheduling: Potential hazards and possible remedies. IEEE Control Systems Magazine, ..."
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Cited by 41 (4 self)
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n Automatic Control, pages 898 907, 1990. J. Shamma and M. Athans. Guaranteed properties of gain scheduled control for linear parametervarying plants. Automatica, pages 559 564, 1991. J. Shamma and M. Athans. Gainscheduling: Potential hazards and possible remedies. IEEE Control Systems Magazine, 12(3):101 107, June 1992. [Sch96] A. Schwartz. Theory and Implementation of Numerical Methods Based on RungeKutta Integration for Optimal Control Problems. PhD Disser tation, University of California, Berkeley, 1996. [SCH+00] M. Sznaier, J. Cloutier, R. Hull, D. Jacques, and C. Mracek. Reced ing horizon control lyapunov function approach to suboptimal regula tion of nonlinear systems. Journal of Guidance, Control, and Dynamics, 23(3):399 405, 2000. [SD90] M. Sznaier and M. J. Damborg. Heuristically enhanced feedback con trol of constrained discretetime linear systems. Automatica, 26:521 532, 1990. [SMR99] P. Scokaert, D. Mayne, and J. Rawlings. Suboptimal model predictive cont
Canonical dual transformation method and generalized triality theory in nonsmooth global optimization
 Journal of Global Optimization
"... Abstract. This paper presents, within a unified framework, a potentially powerful canonical dual transformation method and associated generalized duality theory in nonsmooth global optimization. It is shown that by the use of this method, many nonsmooth/nonconvex constrained primal problems in R n c ..."
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Cited by 17 (9 self)
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Abstract. This paper presents, within a unified framework, a potentially powerful canonical dual transformation method and associated generalized duality theory in nonsmooth global optimization. It is shown that by the use of this method, many nonsmooth/nonconvex constrained primal problems in R n can be reformulated into certain smooth/convex unconstrained dual problems in R m with m � n and without duality gap, and some NPhard concave minimization problems can be transformed into unconstrained convex minimization dual problems. The extended Lagrange duality principles proposed recently in finite deformation theory are generalized suitable for solving a large class of nonconvex and nonsmooth problems. The very interesting generalized triality theory can be used to establish nice theoretical results and to develop efficient alternative algorithms for robust computations.
Superlinear Convergence of PrimalDual Interior Point Algorithms for Nonlinear Programming
, 2000
"... The local convergence properties of a class of primaldual interior point methods are analyzed. These methods are designed to minimize a nonlinear, nonconvex, objective function subject to linear equality constraints and general inequalities. They involve an inner iteration in which the logbarrier ..."
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Cited by 11 (3 self)
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The local convergence properties of a class of primaldual interior point methods are analyzed. These methods are designed to minimize a nonlinear, nonconvex, objective function subject to linear equality constraints and general inequalities. They involve an inner iteration in which the logbarrier merit function is approximately minimized subject to satisfying the linear equality constraints, and an outer iteration that species both the decrease in the barrier parameter and the level of accuracy for the inner minimization. It is shown that, asymptotically, for each value of the barrier parameter, solving a single primaldual linear system is enough to produce an iterate that already matches the barrier subproblem accuracy requirements. The asymptotic rate of convergence of the resulting algorithm is Qsuperlinear and may be chosen arbitrarily close to quadratic. Furthermore, this rate applies componentwise. These results hold in particular for the method described by Conn, Gould, Orb...
NONCONVEX SEMILINEAR PROBLEMS AND CANONICAL DUALITY SOLUTIONS
"... This paper presents a brief review and some new developments on the canonical duality theory with applications to a class of variational problems in nonconvex mechanics and global optimization. These nonconvex problems are directly related to a large class of semilinear partial differential equatio ..."
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Cited by 8 (7 self)
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This paper presents a brief review and some new developments on the canonical duality theory with applications to a class of variational problems in nonconvex mechanics and global optimization. These nonconvex problems are directly related to a large class of semilinear partial differential equations in mathematical physics including phase transitions, postbuckling of large deformed beam model, chaotic dynamics, nonlinear field theory, and superconductivity. Numerical discretizations of these equations lead to a class of very difficult global minimization problems in finite dimensional space. It is shown that by the use of the canonical dual transformation, these nonconvex constrained primal problems can be converted into certain very simple canonical dual problems. The criticality condition leads to dual algebraic equations which can be solved completely. Therefore, a complete set of solutions to these very difficult primal problems can be obtained. The extremality of these solutions are controlled by the socalled triality theory. Several examples are illustrated including the nonconvex constrained quadratic programming. Results show that these very difficult primal problems can be converted into certain simple canonical (either convex or concave) dual problems, which can be solved completely. Also some very interesting new phenomena, i.e. triochaos and metachaos, are discovered in postbuckling of nonconvex systems. The author believes that these important phenomena exist in many nonconvex dynamical systems and deserve to have a detailed study.
Complementarity, polarity and triality in nonsmooth, nonconvex and nonconservative Hamilton systems
"... This paper presents a unified criticalpoint theory in nonsmooth, nonconvex and dissipative Hamilton systems. The canonical dual/polar transformation methods and the associated biduality and triality theories proposed recently in nonconvex variational problems are generalized into fully nonlinea ..."
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Cited by 6 (5 self)
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This paper presents a unified criticalpoint theory in nonsmooth, nonconvex and dissipative Hamilton systems. The canonical dual/polar transformation methods and the associated biduality and triality theories proposed recently in nonconvex variational problems are generalized into fully nonlinear dissipative dynamical systems governed by nonsmooth constitutive laws and boundary conditions. It is shown that, by this method, nonsmooth and nonconvex Hamilton systems can be reformulated into certain smooth dual, complementary and polar variational problems. Based on a newly proposed polar Hamiltonian, a nice bipolarity variational principle is established for threedimensional nonsmooth elastodynamical systems, and a potentially powerful complementary variational principle can be used for solving unilateral variational inequality problems governed by nonsmooth boundary conditions
InteriorPoint Methods
"... this article the motivation for desiring an "interior" path, the concept of the complexity of solving a linear programming problem, a brief history of the developments in the area, and the status of the subject as of this writing are discussed. More complete surveys are given in Gonzaga (1991a,1991b ..."
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Cited by 3 (1 self)
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this article the motivation for desiring an "interior" path, the concept of the complexity of solving a linear programming problem, a brief history of the developments in the area, and the status of the subject as of this writing are discussed. More complete surveys are given in Gonzaga (1991a,1991b,1992), Goldfarb and Todd (1989), Roos and Terlaky (1997), Roos, Terlaky and Vial (1997), Terlaky (1996), Ye (1997), Wright (1996) and Wright (1998). Generalizations to nonlinear problems are briefly discussed as well. For thorough treatment of interior point algorithms on those areas, the reader is referred to den Hertog (1993), Nesterov and Nemirovskii (1993) and Saigal, Vandenberghe and Wolkowicz (1998).
Sensitivity Analysis And The Analytic Central Path
, 1998
"... The analytic central path for linear programming has been studied because of its desirable convergence properties. This dissertation presents a detailed study of the analytic central path under perturbation of both the righthand side and cost vectors for a linear program. The analysis is divided int ..."
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Cited by 2 (1 self)
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The analytic central path for linear programming has been studied because of its desirable convergence properties. This dissertation presents a detailed study of the analytic central path under perturbation of both the righthand side and cost vectors for a linear program. The analysis is divided into three parts: extensions of results required by the convergence analysis when the data is unperturbed to include that case of data perturbation, marginal analysis of the analytic center solution with respect to linear changes in the righthand side, and parametric analysis of the analytic central path under simultaneous changes in both the righthand side and cost vectors. To extend the established convergence results when the data is fixed, it is rst shown that the union of the elements comprising a portion of the perturbed analytic central paths is bounded. This guarantees the existence of subsequences that converge, but these subsequences are not guaranteed to have the same limit without further restrictions on the data movement. Sufficient conditions are provided to insure that the limit is the analytic center of the iii limiting polytope. Furthermore, as long at the data converges and the parameter of the path is approaching zero, certain components of the the analytic central path are forced to zero. Since the introduction of the analytic center to the mathematical programming community, the analytic central path has been known to be analytic in both the righthand side and cost vectors. However, since the objective function is a continuous, piecewise linear function of the righthand side, the analytic center solution is not differentiable. We show that this solution is continuous and is infinitely, continuously, onesided differentiable. Furthermore, the analytic center sol...
Numerical Stability in Linear Programming and Semidefinite Programming
, 2006
"... We study numerical stability for interiorpoint methods applied to Linear Programming, LP, and Semidefinite Programming, SDP. We analyze the di#culties inherent in current methods and present robust algorithms. ..."
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Cited by 1 (1 self)
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We study numerical stability for interiorpoint methods applied to Linear Programming, LP, and Semidefinite Programming, SDP. We analyze the di#culties inherent in current methods and present robust algorithms.
Design of Experiments in Nonlinear Models Asymptotic Normality, Optimality Criteria and SmallSample Properties
"... the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or ..."
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the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication,
ERROR DETECTION WITH REALNUMBER CODES BASED ON RANDOM MATRICES
"... Some wellknown realnumber codes are DFT codes. Since these codes are cyclic, they can be used to correct erasures (errors at known positions) and detect errors, using the locator polynomial via the syndrome, with efficient algorithms. The stability of such codes are, however, very poor for burst e ..."
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Some wellknown realnumber codes are DFT codes. Since these codes are cyclic, they can be used to correct erasures (errors at known positions) and detect errors, using the locator polynomial via the syndrome, with efficient algorithms. The stability of such codes are, however, very poor for burst error patterns. In such conditions, the stability of the system of equations to be solved is very poor. This amplifies the rounding errors inherent to the real number field. In order to improve the stability of realnumber errorcorrecting codes, other types of coding matrices were considered, namely random orthogonal matrices. These type of codes have proven to be very stable, when compared to DFT codes. However, the problem of detecting errors (when the positions of these errors are not known) with random codes was not addressed. Such codes do not possess any specific structure which could be exploited to create an efficient algorithm. In this paper, we present an efficient method to locate errors with codes based on random orthogonal matrices. Index Terms — Error correction, random matrices, real number codes, sparse solutions