##### Department of Mathematics,

University of California San Diego

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### Math 196/296 - Student Colloquium

## Jiawang Nie

#### UCSD

## Hilbert's 17th Problem and Global Optimization

##### Abstract:

This lecture will give a brief introduction of Hilbert's 17th problem: is every nonnegative polynomial a summation of squares of rational functions? After Artin's affirmative solution, there is a generalization to Positivstellensatz on the solvability of semialgebraic systems. The Positivstellensatz can be applied to solve global optimization problems of polynomial functions. The basic tool is semidefinite programming (SDP), a very nice convex optimization model.

### November 25, 2008

### 11:00 AM

### AP&M B412

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