Foundations of Mathematical Optimization

1. Front Matter

   Pages i-xii

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2. General Optimality

   • Diethard Pallaschke, Stefan Rolewicz

   Pages 1-55

3. Optimization in Metric Spaces

   • Diethard Pallaschke, Stefan Rolewicz

   Pages 56-170

4. Multifunctions and marginal functions in metric spaces

   • Diethard Pallaschke, Stefan Rolewicz

   Pages 171-230

5. Well-posedness and weak well-posedness in Banach spaces

   • Diethard Pallaschke, Stefan Rolewicz

   Pages 231-293

6. Duality in Banach and Hilbert spaces. Regularization

   • Diethard Pallaschke, Stefan Rolewicz

   Pages 294-312

7. Necessary conditions for optimality and local optimality in normed spaces

   • Diethard Pallaschke, Stefan Rolewicz

   Pages 313-389

8. Polynomials. Necessary and sufficient conditions of optimality of higher order

   • Diethard Pallaschke, Stefan Rolewicz

   Pages 390-411

9. Nondifferentiable optimization

   • Diethard Pallaschke, Stefan Rolewicz

   Pages 412-468

10. Numerical aspects

    • Diethard Pallaschke, Stefan Rolewicz

    Pages 469-496

11. Vector optimization

    • Diethard Pallaschke, Stefan Rolewicz

    Pages 497-550

12. Back Matter

    Pages 551-585

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Many books on optimization consider only finite dimensional spaces. This volume is unique in its emphasis: the first three chapters develop optimization in spaces without linear structure, and the analog of convex analysis is constructed for this case. Many new results have been proved specially for this publication. In the following chapters optimization in infinite topological and normed vector spaces is considered. The novelty consists in using the drop property for weak well-posedness of linear problems in Banach spaces and in a unified approach (by means of the Dolecki approximation) to necessary conditions of optimality. The method of reduction of constraints for sufficient conditions of optimality is presented. The book contains an introduction to non-differentiable and vector optimization.
Audience: This volume will be of interest to mathematicians, engineers, and economists working in mathematical optimization.

• Approximation
• Mathematica
• optimization
• vector optimization

• Institute for Statistics and Mathematical Economics, University of Karlsruhe, Karlsruhe, Germany

  Diethard Pallaschke

• Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland

  Stefan Rolewicz

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