Morse theory and the algebraic degree of optimization problems

Morse theory and the algebraic degree of optimization problems

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Botong Wang, University of Wisconsin-Madison
Fine Hall 214

Most optimization problems can be reduced to finding the maximum/minimum value of a function on certain space. When both the space and the function are defined by polynomials, we can use algebraic geometry to study the set of all critical points. One particular example is the Euclidean distance degree of an affine variety, which counts the number of critical points of a square distance function. We will discuss some Morse theoretic perspectives of such problems and present an application to the algebraic complexity of a computer vision problem. This is joint work with Laurentiu Maxim and Jose Rodriguez.