The Complexity of Continuous Optimization
Name
MIT-LCS-TM-452.pdf
Size
1.55 MB
Format
Adobe PDF
Checksum (MD5)
0e22dee467a95c96e68f46a745898686
Author(s)
Rogaway, Phillip
Date Issued
June 1991
Series/Report no.
MIT-LCS-TM-452
Abstract
Given a polynomial objective function f(x1,…,xn), we consider the problem of finding the maximum of this polynomial inside some convex set D = {x : Ax <= B}. We show that, under a complexity assumption, this extremum cannot be approximated by any polynomial-time algorithm, even exceedingly poorly. This represents an unusual interplay of discrete and continuous mathematics: using a combinatorial argument to get a hardness result for a continuous optimization problem.
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