Certifying convergence of Lasserre's hierarchy via flat truncation

Optimality conditions and finite convergence of Lasserre's hierarchy

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...

Convergence, Consistency and Stability in Fuzzy Differential Equations

In this paper, we consider First-order fuzzy differential equations with initial value conditions. The convergence, consistency and stability of difference method for approximating the solution of fuzzy differential equations involving generalized H-differentiability, are studied. Then the local truncation error is defined and sufficient conditions for convergence, consistency and stability of ...

Certifying Random Polynomials over the Unit Sphere via Sum of Squares Hierarchy

Given a random n-variate degree-d homogeneous polynomial f , we study the following problem:

COSC460 Honours Report: A Sequential Steady-State Detection Method for Quantitative Discrete-Event Simulation

In quantitative discrete-event simulation, the initial transient phase causes bias in the estimation of steady-state performance measures. Methods for detecting and truncating this phase make calculating accurate estimates from the truncated sample possible, but no methods proposed in the literature have proved to work successfully in the sequential analysis of simulated systems. This report pr...