Hyperbolic Programming (HP) is a generalization of Semidefinite Programming (SDP). Its feasible regions are convex sets that are constrained by hyperbolic polynomials. These multivariate polynomials, closely related to real stable polynomials, extend the linear matrix inequalities that underlie SDP. They arise in many contexts, including negative correlation in probability and exponential families in statistics. This workshop will center around the question: Is HP really more powerful than SDP? This is closely related to recent advances in real algebraic geometry, due to Scheiderer, that are aimed at characterizing which convex sets are spectrahedral shadows. It is also of great interest in theoretical CS, where many of the best-known algorithms for combinatorial optimization are based on SDPs, and beating SDPs in certain contexts is equivalent to refuting the Unique Games Conjecture. This workshop will bring together researchers from these different fields.
Further details about this workshop will be posted in due course. Enquiries may be sent to the organizers workshop-geometry3 [at] lists [dot] simons [dot] berkeley [dot] edu (at this address).
Registration is required to attend this workshop. Space may be limited, and you are advised to register early. The link to the registration form will appear on this page approximately 10 weeks before the workshop. To submit your name for consideration, please register and await confirmation of your acceptance before booking your travel.