In this paper, we solve a class of convex infinite-dimensional optimization problems using a numerical approximation method that does not rely on discretization. Instead, we restrict the decision variable to a sequence of finite-dimensional linear subspaces of the original infinite-dimensional...

We extend the method of Ghasemi and Marshall (SIAM J. Optim. 22(2):460–473, <CitationRef CitationID="CR1">2012</CitationRef>), to obtain a lower bound f <Subscript>gp,M </Subscript> for a multivariate polynomial <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$f(\mathbf{x}) \in\mathbb{R}[\mathbf {x}]$</EquationSource> </InlineEquation> of degree ≤2d in n variables <Emphasis Type="Bold">x=(x <Subscript>1</Subscript>,…,x <Subscript> n </Subscript>) on the closed ball <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\{ \mathbf{x} \in\mathbb{R}^{n} :...</equationsource></inlineequation></subscript></subscript></emphasis></equationsource></inlineequation></subscript></citationref>

The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an...