Ebook: Nonlinear Optimization and Related Topics

This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par­ ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo­ gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume.

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This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the `G. Stampacchia' School of Mathematics of the `E. Majorana' Centre for Scientific Culture, June 23-July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of nonlinear optimization, and of related topics such as convex optimization, nonsmooth optimization, variational inequalities and complementarity problems.

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This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the `G. Stampacchia' School of Mathematics of the `E. Majorana' Centre for Scientific Culture, June 23-July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of nonlinear optimization, and of related topics such as convex optimization, nonsmooth optimization, variational inequalities and complementarity problems.
Content:
Front Matter....Pages i-vii
Generalized Lagrange multipliers: regularity and boundedness....Pages 1-14
A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints....Pages 15-49
Minimal Convexificators of a positively Homogeneous Function and a Characterization of Its Convexity and Concavity....Pages 51-65
Optimal Control Problems and Penalization....Pages 67-78
A truncated Newton method for constrained optimization....Pages 79-103
Fixed and virtual stability center methods for convex nonsmooth minimization....Pages 105-122
Iterative methods for ill-conditioned linear systems from optimization....Pages 123-141
An Algorithm for Solving Nonlinear Programs with Noisy Inequality Constraints....Pages 143-167
Generic Existence, Uniqueness and Stability in Optimization Problems....Pages 169-182
On a class of bilevel programs....Pages 183-206
Separation methods for Vector Variational Inequalities. Saddle point and gap function....Pages 207-217
Functions with Primal-Dual Gradient Structure and u-Hessians....Pages 219-233
Quadratic and Multidimensional Assignment Problems....Pages 235-256
A new merit function and an SQP method for non-strictly monotone variational inequalities....Pages 257-275
A Logarithmic Barrier Approach to Fischer Function....Pages 277-297
On an Approach to Optimization Problems with a Probabilistic Cost and or Constraints....Pages 299-315
Semiderivative Functions and Reformulation Methods for Solving Complementarity and Variational Inequality Problems....Pages 317-350
Global Lagrange multiplier rule and smooth exact penalty functions for equality constraints....Pages 351-368
Structural Methods in the Solution of Variational Inequalities....Pages 369-380
Extended Nonlinear Programming....Pages 381-399
On the Efficiency of Splitting and Projection Methods for Large Strictly Convex Quadratic Programs....Pages 401-413
A Comparison of Rates of Convergence of Two Inexact Proximal Point Algorithms....Pages 415-427
One way to Construct a Global Search Algorithm for d.c. Minimization Problems....Pages 429-443
Error Bounds and Superlinear Convergence Analysis of Some Newton-Type Methods in Optimization....Pages 445-462
A New Derivative-Free Descent Method for the Nonlinear Complementarity Problem....Pages 463-487
Back Matter....Pages 489-491

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This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the `G. Stampacchia' School of Mathematics of the `E. Majorana' Centre for Scientific Culture, June 23-July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of nonlinear optimization, and of related topics such as convex optimization, nonsmooth optimization, variational inequalities and complementarity problems.
Content:
Front Matter....Pages i-vii
Generalized Lagrange multipliers: regularity and boundedness....Pages 1-14
A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints....Pages 15-49
Minimal Convexificators of a positively Homogeneous Function and a Characterization of Its Convexity and Concavity....Pages 51-65
Optimal Control Problems and Penalization....Pages 67-78
A truncated Newton method for constrained optimization....Pages 79-103
Fixed and virtual stability center methods for convex nonsmooth minimization....Pages 105-122
Iterative methods for ill-conditioned linear systems from optimization....Pages 123-141
An Algorithm for Solving Nonlinear Programs with Noisy Inequality Constraints....Pages 143-167
Generic Existence, Uniqueness and Stability in Optimization Problems....Pages 169-182
On a class of bilevel programs....Pages 183-206
Separation methods for Vector Variational Inequalities. Saddle point and gap function....Pages 207-217
Functions with Primal-Dual Gradient Structure and u-Hessians....Pages 219-233
Quadratic and Multidimensional Assignment Problems....Pages 235-256
A new merit function and an SQP method for non-strictly monotone variational inequalities....Pages 257-275
A Logarithmic Barrier Approach to Fischer Function....Pages 277-297
On an Approach to Optimization Problems with a Probabilistic Cost and or Constraints....Pages 299-315
Semiderivative Functions and Reformulation Methods for Solving Complementarity and Variational Inequality Problems....Pages 317-350
Global Lagrange multiplier rule and smooth exact penalty functions for equality constraints....Pages 351-368
Structural Methods in the Solution of Variational Inequalities....Pages 369-380
Extended Nonlinear Programming....Pages 381-399
On the Efficiency of Splitting and Projection Methods for Large Strictly Convex Quadratic Programs....Pages 401-413
A Comparison of Rates of Convergence of Two Inexact Proximal Point Algorithms....Pages 415-427
One way to Construct a Global Search Algorithm for d.c. Minimization Problems....Pages 429-443
Error Bounds and Superlinear Convergence Analysis of Some Newton-Type Methods in Optimization....Pages 445-462
A New Derivative-Free Descent Method for the Nonlinear Complementarity Problem....Pages 463-487
Back Matter....Pages 489-491
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