Line-then-plane optimization

A related idea is used in the Line Then Plane (LTP) algorithm where the constrained optimization is done in the hyperplane perpencheular to the interpolation line between the two end-points, rather than on a hypersphere. 

Line Then Plane ILTP) optimization method. MMFF force held, 40 One-electron integrals, 67 Powell update, for optimizations. 321 ... 

Two-structure interpolation methods saddle, line-then-plane, ridge and step-and-slide optimizations... 

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. 

The idea in the line then plane (LTP) algorithm is similar to the saddle method, but the constrained optimization is done in the hypeiplane perpendicular to the inteipolation line between the two end-points, rather than on a hypersphere. LTP may also be considered as a variation of LUP where only two intermediate points are used, and the end-points are discarded after each minimization. This is iliustrated in Figure 7. 

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