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radient method Newton s method to amend Quasi-Newton Method trust region method explicitly steepest descent method, Rosen gradient projection method Penalty function method outside the penalty function method within the penalty function method Mixed penalty function multiplier method G-N was amended in G-N method L-M method Of linear programming simplex method, revised simplex method Big M method variables bounded simplex method, Cutting Plane Method integer programming branch and bound method 0-1 programming quadratic programming