Nondifferentiable Optimization: Motivations and Applications

1. Front Matter

   Pages N2-VI

   PDF

2. Concepts in Nonsmooth Analysis

   1. Front Matter

      Pages 1-1

      PDF

   2. Attempts to Approximate a Set-Valued Mapping

      • V. F. Demyanov, C. Lemaréchal, J. Zowe

      Pages 3-7

   3. Miscellanies on Nonsmooth Analysis and Optimization

      • J.-B. Hiriart-Urruty

      Pages 8-24

   4. Bundle Methods, Cutting-Plane Algorithms and σ-Newton Directions

      • C. Lemaréchal, J. J. Strodiot

      Pages 25-33

   5. The Solution of a Nested Nonsmooth Optimization Problem

      • Robert Mifflin

      Pages 34-40

   6. Variations on the Theme of Nonsmooth Analysis: Another Subdifferential

      • Jean-Paul Penot

      Pages 41-54

   7. Lipschitzian Stability in Optimization: The Role of Nonsmooth Analysis

      • R. T. Rockafellar

      Pages 55-73

   8. Upper-Semicontinuously Directionally Differentiable Functions

      • A. M. Rubinov

      Pages 74-86

   9. A New Approach to Clarke’s Gradients in Infinite Dimensions

      • Jay S. Treiman

      Pages 87-93

3. Multicriteria Optimization and Control Theory

   1. Front Matter

      Pages 95-95

      PDF

   2. A Nondifferentiable Approach to Multicriteria Optimization

      • Y. Evtushenko, M. Potapov

      Pages 97-102

   3. Application of a Subdifferential of a Convex Composite Functional to Optimal Control in Variational Inequalities

      • B. Lemaire

      Pages 103-117

   4. On Some Nondifferentiable Problems in Optimal Control

      • J. V. Outrata, Z. Schindler

      Pages 118-128

   5. On Sufficient Conditions for Optimality of Lipschitz Functions and Their Applications to Vector Optimization

      • S. Rolewicz

      Pages 129-138

   6. Optimal Control of Hyperbolic Variational Inequalities

      • Dan Tiba

      Pages 139-149

   7. On Duality Theory Related to Approximate Solutions of Vector-Valued Optimization Problems

      • István Vályi

      Pages 150-162

4. Algorithms and Optimization Methods

   1. Front Matter

      Pages 163-163

      PDF

   2. Seminormal Functions in Optimization Theory

      • E. J. Balder

      Pages 165-169

   3. The General Concept of Cone Approximations in Nondifferentiable Optimization

      • K.-H. Elster, J. Thierfelder

      Pages 170-189

The International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Austria, has been involved in research on nondifferentiable optimization since 1976. IIASA-based East-West cooperation in this field has been very productive, leading to many important theoretical, algorithmic and applied results. Nondifferentiable optimi­ zation has now become a recognized and rapidly developing branch of mathematical programming. To continue this tradition, and to review recent developments in this field, IIASA held a Workshop on Nondifferentiable Optimization in Sopron (Hungary) in September 1964. The aims of the Workshop were: 1. To discuss the state-of-the-art of nondifferentiable optimization (NDO), its origins and motivation; 2. To compare-various algorithms; 3. To evaluate existing mathematical approaches, their applications and potential; 4. To extend and deepen industrial and other applications of NDO. The following topics were considered in separate sessions: General motivation for research in NDO: nondifferentiability in applied problems, nondifferentiable mathematical models. Numerical methods for solving nondifferentiable optimization problems, numerical experiments, comparisons and software. Nondifferentiable analysis: various generalizations of the concept of subdifferen­ tials. Industrial and other applications. This volume contains selected papers presented at the Workshop. It is divided into four sections, based on the above topics: I. Concepts in Nonsmooth Analysis II. Multicriteria Optimization and Control Theory III. Algorithms and Optimization Methods IV. Stochastic Programming and Applications We would like to thank the International Institute for Applied Systems Analysis, particularly Prof. V. Kaftanov and Prof. A.B. Kurzhanski, for their support inorganiz­ ing this meeting.

• Applications
• Optimization Methods
• algorithms
• cooperation
• duality
• linear optimization
• mathematical programming
• optimization
• optimization theory
• planning
• programming
• research
• science and technology
• stability
• variational inequalities

• International Institute for Applied Systems Analysis, Laxenburg, Austria

  Vladimir F. Demyanov

• Applied Mathematical Department, Leningrad University, Leningrad, USSR

  Vladimir F. Demyanov

• Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Karlsruhe 1, Germany

  Diethard Pallaschke

Policies and ethics