Dido's Problem and Pareto Optimality

S. S. Kutateladze

An expanded version of the talk is available in PDF

The extremal problems, generously populating all branches of mathematics, use only scalar targets. Problems with many objectives have become the topic of research rather recently and noticeably beyond mathematics, which explains the substantial gap between the levels of complexity and power of the mathematical tools available for single objective and multiple objective problems. This challenges the task of enriching the stock of vector optimization problems within the theoretical core of mathematics.
Under study is the class of geometrically meaningful vector optimization problems whose solutions can be found explicitly to some extend in terms of conditions on surface area measures. The positivy technique of settling the extremal problems of convex geometry is still insufficiently popular, while bridging the gaps between mathematics and the art and science of multiple criteria decision making.

This talk was delivered at the International Conference Positivity VI, El Escorial, Spain on July 21, 2009.

Slides in PDF.

El Escorial, 2009

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File translated from TEX by TTH, version 3.77.
On 30 June 2009, 20:47.

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