Locally updated planes minimization

The Locally Updated Plane.s- (LUP) minimization is related to the chain method, but the relaxation is here done in the hyperplane perpendieular to the reaction coordinate, rather than along a line defined by the gradient. Furthermore, all the points are moved in each iteration, rather than one at a time. 

N C The Locally Updated Planes (LUP) minimization " is related to the chain method, but... 

The locally updated planes (LUP) method also optimizes a chain of points simultaneously. For each point x, along the pathway, a hyperplane orthogonal to the path is defined. The points are then energy minimized with the constraint that each has to remain in its initial plane. The planes are periodically updated to account for the changing shape of the path. The LUP algorithm is ideally suited for refining a chain that is already near the adiabatic path. 

CPR = conjugate peak refinement GDIIS = geometry direct inversion in the iterative subspace GE = gradient extremal LST = linear synchronous transit LTP = line then plane LUP = locally updated planes NR = Newton-Raph-son P-RFO = partitioned rational function optimization QA = quadratic approximation QST = quadratic synchronous transit SPW = self-penalty walk STQN = synchronous transit-guided quasi-Newton TRIM = trust radius image minimization TS = transition structure. 

---