BOOKMARK & SHARE
ACM Transactions on Mathematical Software (TOMS): Volume 43 Issue 4, March 2017
Citation Count: 0
Downloads (6 Weeks): 12, Downloads (12 Months): 88, Downloads (Overall): 88
Full text available:
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance, for FPGAs or custom hardware implementations. This problem becomes challenging when the program does not employ solely ...
floating-point arithmetic, polynomial optimization, Correlation sparsity pattern, roundoff error, semidefinite programming, transcendental functions, formal verification, proof assistant
Mathematical Programming: Series A and B: Volume 151 Issue 2, July 2015
Publisher: Springer-Verlag New York, Inc.
We consider the problem of certifying lower bounds for real-valued multivariate transcendental functions. The functions we are dealing with are nonlinear and involve semialgebraic operations as well as some transcendental functions like $$\cos ,\,\arctan ,\,\exp $$cos,arctan,exp, etc. Our general framework is to use different approximation methods to relax the original ...
90C59, Nonlinear template method, Polynomial optimization problems, 41A10, Certified global optimization, Semialgebraic relaxations, Semidefinite programming, 41A50, 90C22, 11E25, 90C26, Maxplus approximation
Operations Research Letters: Volume 42 Issue 6, September, 2014
Publisher: Elsevier Science Publishers B. V.
We approximate as closely as desired the Pareto curve associated with bicriteria polynomial optimization problems. We use three formulations (including the weighted sum approach and the Chebyshev approximation) and each of them is viewed as a parametric polynomial optimization problem. For each case is associated a hierarchy of semidefinite relaxations ...
Pareto curve, Sums of squares relaxations, Inverse problem from generalized moments, Parametric polynomial optimization problems, Multicriteria optimization, Semidefinite programming
CICM'13: Proceedings of the 2013 international conference on Intelligent Computer Mathematics
The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture ...
flyspeck project, max-plus approximation, quadratic cuts, semialgebraic relaxations, semidefinite programming, transcendental functions, hybrid symbolicnumeric certification, polynomial optimization problems, proof assistant, templates method