- Alexandrov, N. and Dennis, J.E., 1999: A Class of General Trust Region Multilevel Algorithms for Systems of Nonlinear Equations and Equality Constrained Optimization: Global Convergence Theory, SIAM Journal on Optimization, (in review). Home/Search Document Details and Download
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Algorithms for Bilevel Optimization - Alexandrov, Dennis, Jr. (1994) (2 citations) Self-citation (Alexandrov Dennis) (Correct)
....bilevel optimization (see Vicente and Calamai [18] for a review) deals only with functions under extremely strong assumptions of convexity and has many theoretical difficulties. We are approaching this problem with cautious optimism because in recent work (see Alexandrov [1] Alexandrov and Dennis [2], 3] algorithms for multilevel optimization of problems with special structure have been shown to exhibit global convergence under reasonable assumptions. In this paper we will use the general bilevel optimization problem to discuss issues in MLO. First, we remark in passing that for the two ....
.... and Byrd [13] Multilevel Methods for Nonlinear Equations and Equality Constrained Optimization The algorithms introduced here are based on the recently proposed class of multilevel algorithms for equality constrained optimization and nonlinear equations (see Alexandrov [1] Alexandrov and Dennis [2], 3] The algorithms of that class use trust regions as a globalization startegy, they have been shown to be globally convergent under reasonable assumptions. They have the following characteristics: ffl The constraints of the problem can be partitioned into blocks by the user in any manner ....
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Natalia Alexandrov and J. E. Dennis, Jr. A class of general trust-region multilevel algorithms for systems of nonlinear equations: Global convergence theory. In preparation.
Multilevel Algorithms for Nonlinear Optimization - Alexandrov, Dennis, Jr. (1994) (3 citations) Self-citation (Alexandrov Dennis) (Correct)
....in formulations can be found in [5] and [11] Some of the approaches in [5] have been proven to be successful for many problems. In order to be more widely applicable, it requires the development of theoretical foundations. We propose a class of multilevel optimization methods (see [2] [3]) for solving the nonlinear equality constrained optimization problem characterized by the following features: ffl The constraints of the problem can be partitioned into blocks in any manner suitable to an application, or in any arbitrary manner at all. The analysis of the methods assumes certain ....
....optimization algorithms for the nonlinear equality constrained minimization problem. Since the time of its introduction in [2] the class has undergone changes. In [2] the globalization and extension to constrained optimization only of local Brent s method was proposed. Recent developments (see [3]) have extended the results to provide globalization and extension to constrained optimization of the entire local Brown Brent class. 3.1 Notation Due to arbitrary blocking of the constraints, the notation becomes cumbersome. To ease the reading effort, we omit the subscripts and superscripts ....
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Natalia Alexandrov and J. E. Dennis, Jr. A class of general trust-region multilevel algorithms for systems of nonlinear equations: Global convergence theory. In preparation.
Constructing Variable Fidelity Response Surface.. - Pérez, Renaud, Gano (2000) (Correct)
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- Alexandrov, N. and Dennis, J.E., 1999: A Class of General Trust Region Multilevel Algorithms for Systems of Nonlinear Equations and Equality Constrained Optimization: Global Convergence Theory, SIAM Journal on Optimization, (in review).
Convergence of trust region augmented Lagrangian.. - Rodríguez.. (Correct)
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Alexandrov, N.; Dennis J. E. 1997: A Class of General Trust-Region Multilevel Algorithms for Systems of Nonlinear Equations and Equality Constrained Optimization: Global Convergence Theory. Submitted to SIAM Journal on Optimization.
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