Near-optimal analysis of Lasserre’s univariate measure-based bounds for multivariate polynomial optimization
نویسندگان
چکیده
منابع مشابه
Convergence analysis for Lasserre's measure-based hierarchy of upper bounds for polynomial optimization
We consider the problem of minimizing a continuous function f over a compact set K. We analyze a hierarchy of upper bounds proposed by Lasserre in [SIAM J. Optim. 21(3) (2011), pp. 864−885], obtained by searching for an optimal probability density function h on K which is a sum of squares of polynomials, so that the expectation ∫ K f(x)h(x)dx is minimized. We show that the rate of convergence i...
متن کاملComparison of Lasserre’s measure–based bounds for polynomial optimization to bounds obtained by simulated annealing
We consider the problem of minimizing a continuous function f over a compact set K. We compare the hierarchy of upper bounds proposed by Lasserre in [SIAM J. Optim. 21(3) (2011), pp. 864− 885] to bounds that may be obtained from simulated annealing. We show that, when f is a polynomial and K a convex body, this comparison yields a faster rate of convergence of the Lasserre hierarchy than what w...
متن کاملA Polynomial Algorithm for Optimal Univariate Microaggregation
Microaggregation is a technique used by statistical agencies to limit disclosure of sensitive microdata. Noting that no polynomial algorithms are known to microaggregate optimally, Domingo-Ferrer and Mateo-Sanz have presented heuristic microaggregation methods. This paper is the first to present an efficient polynomial algorithm for optimal univariate microaggregation. Optimal partitions are sh...
متن کاملOn Bounds For The Zeros of Univariate Polynomial
Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated. Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds fo...
متن کاملApproximate Optimal Designs for Multivariate Polynomial Regression
Abstract: We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically the approximate optimal design problem. The geometry of the design is recovered via semidefinite programming duality theory. Th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2020
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-020-01586-y