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VERSION:2.0
PRODID:-//University of Liverpool Computer Science Seminar System//v2//EN
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DTSTAMP:20260918T224406Z
UID:Seminar-EcCo-589@lxserverM.csc.liv.ac.uk
ORGANIZER:CN=Nicos 	Protopapas:MAILTO:N.Protopapas@liverpool.ac.uk
DTSTART:20181205T130000
DTEND:20181205T140000
SUMMARY:Economics and Computation Series
DESCRIPTION:Themistoklis Melissourgos: Approximating the Existential Theory of the Reals\n\nThe existential theory of the reals (ETR) consists of existentially quantified boolean formulas over equalities and inequalities of real-valued polynomials. We propose the approximate existential theory of the reals (epsilon-ETR), in which the constraints only need to be satisfied approximately. We first show that unconstrained epsilon-ETR = ETR, and then study the epsilon-ETR problem when the solution is constrained to lie in a given convex set. Our main theorem is a sampling theorem, similar to those that have been proved for approximate equilibria in normal form games. It states that if an ETR problem has an exact solution, then it has a k-uniform approximate solution, where k depends on various properties of the formula. A consequence of our theorem is that we obtain a quasi-polynomial time approximation scheme (QPTAS) for a fragment of constrained epsilon-ETR. We use our theorem to create several new PTAS and QPTAS algorithms for problems from a variety of fields.\n\nJoint work with Argyrios Deligkas, John Fearnley, and Paul Spirakis.\nTo appear in WINE '18.\n\nhttps://www.csc.liv.ac.uk/research/seminars/abstract.php?id=589
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