# Optimization Theory and Related Topics

Share this page *Edited by *
*Simeon Reich; Alexander J. Zaslavski*

A co-publication of the AMS and Bar-Ilan University

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.

# Table of Contents

## Optimization Theory and Related Topics

- Preface vii8 free
- Biography and Bibliography of Dan Butnariu ix10 free
- Conference Program xv16 free
- Sensitivity Estimates Via Lyapunov Functions and Lyapunov Metrics 122 free
- On the Maximal Monotonicity of the Sum of a Maximal Monotone Linear Relation and the Subdifferential Operator of a Sublinear Function 1940
- An Inverse Newton Transform 2748
- Infinite-Horizon Discrete-Time Pontryagin Principles via Results of Michel 4162
- On Sharing of Risk and Resources 5374
- The Expected Retraction Method in Banach Spaces 6990
- Solution of a Singular Optimal Control Problem with State Delays: A Cheap Control Approach 7798
- Robust Reduction of Dimension of a Linear Programming Problem with Uncertainties: Implication for Robust Production and Technology Planning 109130
- 1. Introduction 109130
- 2. LP model 110131
- 3. Box-constrained uncertainty 111132
- 4. Finding redundant rows 111132
- 5. Equivalent transformation 112133
- 6. Robust upper bounds for dual variables 113134
- 7. Lower bound for an objective 114135
- 8. Who will get investments? 114135
- 9. More lower bounds 114135
- 10. More upper bounds 115136
- 11. Finding redundant columns 115136
- 12. Numerical examples 116137
- 13. Conclusion 118139
- References 118139

- Descent Methods for Mixed Variational Inequalities with Non-Smooth Mappings 121142
- 1. Introduction 121142
- 2. Preliminaries 123144
- 3. Properties of gap functions 126147
- 4. Stationarity and construction of descent directions 128149
- 5. Descent algorithm with exact linesearch 130151
- 6. Descent algorithm with inexact linesearch 132153
- 7. Modified descent algorithm with inexact linesearch 133154
- 8. Combined descent and proximal point methods 135156
- References 136157

- A Generalized Möbius Transform of Games on MV-algebras and Its Application to a Cimmino-type Algorithm for the Core 139160
- Ergodic Convergence in Subgradient Optimization with Application to Simplicial Decomposition of Convex Programs 159180
- 1. Introduction and background 160181
- 2. Basic convergence results 161182
- 3. Applications of the basic convergence results 165186
- 4. Related work: ergodic convergence for Lagrangian and saddle point problems 174195
- 5. A simplicial decomposition scheme for non-smooth minimization 175196
- 6. Concluding remarks 185206
- References 186207

- Strategic Behavior in Multiple-Period Financial Markets 191212
- The Bregman Distance without the Bregman Function II 213234
- Three Strong Convergence Theorems Regarding Iterative Methods for Solving Equilibrium Problems in Reflexive Banach Spaces 225246
- Towards Using Coderivatives for Convergence Rates in Regularization 241262
- Existence of Exact Penalty in Constrained Optimization and the Mordukhovich Basic Subdifferential 251272
- Weakly Agreeable Programs for the Robinson-Solow-Srinivasan (RSS) Model 259280