Secant Update generalized version of PSB: a new approach

In optimization, one of the main challenges widely used family Quasi-Newton methods is to find an estimate Hessian matrix as close possible real matrix. this paper, we develop a new update formula for starting from Powell-Symetric-Broyden (PSB) and adding pieces information previous steps optimization path. This lead multisecant version PSB, which call generalised PSB (gPSB), but does not exist in general was proven before. We provide novel interpretation non-existence. addition, that satisfies condition symmetric vice versa second formula. Subsequently, add enforcement last secant equation present comparison between different methods.