Jonathan Hauenstein; Opti­miza­tion and Numer­i­cal Alge­braic Geometry

October 28, 2014, 4:00pm
GUG 204
Jonathan Hauenstein, Depart­ment of Applied and Com­pu­ta­tional Math­e­mat­ics and Sta­tis­tics, Uni­ver­sity of Notre Dame.
Opti­miza­tion and Numer­i­cal Alge­braic Geometry

Abstract: Classically, one can observe the combination of algebraic geometry and optimization in solving polynomial systems constructed from necessary condition of polynomial optimization problems. More recently, the connection between semidefinite programming and real algebraic geometry has been exploited. This talk will explore another use of optimization related to algebraic geometry, namely to construct homotopies in numerical algebraic geometry for solving polynomial systems. This idea has been used recently to solve a problem in real enumerative geometry. This talk will conclude with using algebraic geometry to solve sparse optimization problems arising from the concept of matrix rigidity. To incorporate a broad audience, all necessary concepts related to algebraic geometry and homotopies will be covered.

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