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>

In this paper, we propose a method of determining the initial temperature for continuous fast simulated annealing from the perspective of state variation. While the conventional method utilizes fitness variation, the proposed method additionally considers genotype variation. The proposed scheme...

The solution of PDE-constrained optimal control problems is a computationally challenging task, and it involves the solution of structured algebraic linear systems whose blocks stem from the discretized first-order optimality conditions. In this paper we analyze the numerical solution of this...