Fractional programming - a survey (Q1106105)

A fractional program maximizes or minimizes a ratio of two linear, or nonlinear, functions. Such programs arise, Upr. 8, 105-114 (1986). A game of planar pursuit with dynamics described by the equations \(\dot x^ i=v^ i \cos \phi^ i\), \(\dot\phi^ i=u^ i\) \((i=1,2)\), and \(\dot y^ i=v^ i \sin \phi^ i\), \(v^ 1>v^ 2\), \(| u^ i| \leq \bar u^ i<\infty\) is considered. Attainability functions are constructed and an optimal closed-looped strategy for the pursuer is found.