This paper develops a Bregman operator splitting algorithm with variable stepsize (BOSVS) for solving problems of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\min\{\phi(Bu) +1/2\|Au-f\|_{2}^{2}\}$</EquationSource> </InlineEquation>, where ϕ may be nonsmooth. The original Bregman Operator Splitting (BOS) algorithm employed a fixed stepsize, while BOSVS uses a...</equationsource></inlineequation>

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>