# Algorithms for Worst-Case Design and Applications to Risk Management

By Berç Rustem; Melendres Howe | Go to book overview

Chapter 5
Numerical experiments with continuous minimax
algorithms

In this chapter, we consider the implementation of continuous minimax algorithms. The first is the gradient-based algorithm due to Kiwiel (1987), discussed in Section 2. 4, and the second is the quasi-Newton algorithm in Chapter 4, and a simplified variant derived from this algorithm.

An important complication of continuous minimax is the presence of multiple maximizers. The contribution of these maximizers to the definition of the direction of search of an algorithm is often difficult to evaluate. We consider several strategies suggested by these algorithms for this purpose. The utility of adopting a simplified direction is evaluated. In addition, the general performance of the algorithms are considered in terms of termination criteria, accuracy of the solution and convergence rates.

We observe a superior performance of the full quasi-Newton algorithm and promising results obtained by adopting the variant with a simplified search direction, not requiring convex combination of subgradients.

1 INTRODUCTION

As in Chapters 3 and 4, we consider the continuous minimax problem, constrained in y, but unconstrained in x

and express it as where Φ(x) is the max-function The vector x is defined on the n-dimensional Euclidian space, Y is a convex compact set, f(x, y) is continuous in x, y and twice continuously differentiable in x. In this chapter, we discuss numerical experience using two versions of a quasi-Newton algorithm and Kiwiel's (1987) algorithm for continuous mini-

-93-

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes

#### Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Note: primary sources have slightly different requirements for citation. Please see these guidelines for more information.

#### Cited page

Algorithms for Worst-Case Design and Applications to Risk Management

• Title Page *
• Algorithms for Worst-Case Design and Applications to Risk Management *
• Contents vii
• Preface xiii
• Chapter 1 - Introduction to Minimax 1
• References 17
• Comments and Notes *
• Chapter 2 - A Survey of Continuous Minimax Algorithms 23
• References *
• Comments and Notes *
• Chapter 3 - Algorithms for Computing Saddle Points 37
• References *
• Comments and Notes *
• Chapter 4 - A Quasi-Newton Algorithm for Continuous Minimax 63
• References *
• Appendix A - Implementation Issues *
• Appendix B - Motivation for the Search Direction D̄ *
• Comments and Notes *
• Chapter 5 - Numerical Experiments with Continuous Minimax Algorithms 93
• References 119
• Chapter 6 - Minimax as a Robust Strategy for Discrete Rival Scenarios 121
• References *
• Chapter 7 - Discrete Minimax Algorithm for Equality and Inequality Constrained Models 139
• References *
• Chapter 8 - A Continuous Minimax Strategy for Options Hedging 179
• References *
• Appendix A - Weighting Hedge Recommendations, Variant B* *
• Appendix B - Numerical Examples 237
• Comments and Notes 244
• Chapter 9 - Minimax and Asset Allocation Problems 247
• References *
• Comments and Notes *
• Chapter 10 - Asset/liability Management under Uncertainty 291
• References *
• Comments and Notes *
• Chapter 11 - Robust Currency Management 341
• References *
• Appendix - Currency Forecasting *
• Comments and Notes *
• Index 381
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this book
• Bookmarks
• Highlights & Notes
• Citations
/ 389

## Questia reader help

### How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

## Cited passage

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.