Efficient algorithms for solving rank two and rank three bilinear programming problems (Q1186269)

A rank \(k\) bilinear programming problem is a nonconvex quadratic programming problem with the following structure: minimize \(\left\{c^ t_ 0 x+d^ t_ 0 y+\sum^ k_{j=1} c^ t_ j x\cdot d^ t_ j y\mid x\in X, y\in Y\right\}\), where \(X\subset R^ n\) and \(Y\subset R^ n\) are non-empty and bounded polytopes. The authors show that a variant of the parametric simplex algorithm can solve large-scale rank two bilinear programming problems efficiently. Also, they show that a cutting-cake-algorithm, a more elaborate variant of parametric simplex algorithm can solve medium-scale rank three problems.