Optimization theory and related topics : Israel mathematical conference proceedings, a workshop in memory of Dan Butnariu, January 11-14, 2010, Haifa, Israel / Simeon Reich, Alexander J. Zaslavski, editors.

Format:

Book

Contributor:

Butnariu, Dan, honouree.

Reich, Simeon, editor.

Zaslavski, Alexander J., editor.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 568

Contemporary mathematics, 568 0271-4132

Language:

English

Subjects (All):

Mathematical optimization--Congresses.

Mathematical optimization.

Differential equations--Congresses.

Differential equations.

Physical Description:

1 online resource (296 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society ; Ramat Gan, Israel : Bar-Ilan University, [2012]

Language Note:

English

Summary:

This volume contains the proceedings of the workshop on Optimization Theory and Related Topics, held in memory of Dan Butnariu, from January 11-14, 2010, in Haifa, Israel. An active researcher in various fields of applied mathematics, Butnariu published over 80 papers. His extensive bibliography is included in this volume. The articles in this volume cover many different areas of Optimization Theory and its applications: maximal monotone operators, sensitivity estimates via Lyapunov functions, inverse Newton transforms, infinite-horizon Pontryagin principles, singular optimal control problems with state delays, descent methods for mixed variational inequalities, games on MV-algebras, ergodic convergence in subgradient optimization, applications to economics and technology planning, the exact penalty property in constrained optimization, nonsmooth inverse problems, Bregman distances, retraction methods in Banach spaces, and iterative methods for solving equilibrium problems. This volume will be of interest to both graduate students and research mathematicians.

Contents:

Preface

Biography and Bibliography of Dan Butnariu

Conference Program

Sensitivity Estimates Via Lyapunov Functions and Lyapunov Metrics

1. Introduction

2. Contraction-like mappings

3. Lyapunov metrics

4. Construction of Lyapunov metrics

5. Equivalence of the metrics

6. Error estimates for fixed points

7. Error estimates for trajectories

References

On the Maximal Monotonicity of the Sum of a Maximal Monotone Linear Relation and the Subdifferential Operator of a Sublinear Function

2. Auxiliary Results

3. Main Result

Acknowledgment

An Inverse Newton Transform

2. Results

3. Examples

4. The logistic iteration

5. Complex iterations

Infinite-Horizon Discrete-Time Pontryagin Principles via Results of Michel

2. Conditions and recall

3. Weak Pontryagin principles

4. Strong Pontryagin principles

5. Proof of Theorem 3.1

6. Proof of Theorem 3.2

7. Proofs of Theorem 4.1 and Theorem 4.2

On Sharing of Risk and Resources

2. An Example

3. Efficient Sharing under Possibly Non-convex Preferences

4. Risk Sharing

5. Efficient Sharing as a Differential System

6. Who should actively share?

7. Concluding Remarks

The Expected Retraction Method in Banach Spaces

2. Definitions

3. The expected retraction operator

4. The relaxed expected retraction operator

5. ERM iterations

Solution of a Singular Optimal Control Problem with State Delays: A Cheap Control Approach

2. Problem statement and main assumptions

3. Regularization of the OOCP

4. Asymptotic solution of the CCP

5. Main results

Robust Reduction of Dimension of a Linear Programming Problem with Uncertainties: Implication for Robust Production and Technology Planning

2. LP model

3. Box-constrained uncertainty

4. Finding redundant rows

5. Equivalent transformation

6. Robust upper bounds for dual variables

7. Lower bound for an objective

8. Who will get investments?

9. More lower bounds

10. More upper bounds

11. Finding redundant columns

12. Numerical examples

13. Conclusion

Descent Methods for Mixed Variational Inequalities with Non-Smooth Mappings

2. Preliminaries

3. Properties of gap functions

4. Stationarity and construction of descent directions

5. Descent algorithm with exact linesearch

6. Descent algorithm with inexact linesearch

7. Modified descent algorithm with inexact linesearch

8. Combined descent and proximal point methods

References.

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-8778-5