Given symmetric matrices B,D∈ℝ<Superscript> n×n </Superscript> and a symmetric positive definite matrix W∈ℝ<Superscript> n×n </Superscript>, maximizing the sum of the Rayleigh quotient <Emphasis Type="Bold">x <Superscript>⊤</Superscript> D <Emphasis Type="Bold">x and the generalized Rayleigh quotient <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\frac{\mathbf{x}^{\top}B \mathbf{x}}{\vphantom{\mathrm{I}^{\mathrm{I}}}\mathbf{x}^{\top}W\mathbf{x} }$</EquationSource> </InlineEquation>...</equationsource></inlineequation></emphasis></superscript></emphasis></superscript></superscript>

In this paper, we propose a robust sequential quadratic programming (SQP) method for nonlinear programming without using any explicit penalty function and filter. The method embeds the modified QP subproblem proposed by Burke and Han (Math Program 43:277–303, <CitationRef CitationID="CR9">1989</CitationRef>) for the search direction,...</citationref>

This paper presents a modified descent method for solving co-coercive variational inequalities. Incorporating with the techniques of identifying descent directions and optimal step sizes along these directions, the new method improves the efficiencies of some existing projection methods. Some...