Stochastic polynomial optimization

ABSTRACT

This paper studies stochastic optimization problems with polynomials. We propose an optimization model with sample averages and perturbations. The Lasserre-type Moment-SOS relaxations are used to solve the sample average optimization. Properties of the optimization and its relaxations are studied. Numerical experiments are presented.

KEYWORDS:

• Stochastic optimization
• polynomial
• moment-SOS relaxation
• semidefinite program

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 90C15
• 90C22
• 90C31
• 65K05

Notes

1 For sets $A,B\subseteq {\mathbb{R}}^n$, their distance is defined as $\text{dist}(A,B):=max\left\{\underset{x\in A}{sup}\underset{y\in B}{inf}\parallel x-y\parallel ,\underset{x\in B}{sup}\underset{y\in A}{inf}\parallel x-y\parallel \right\}.$