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Dual algorithms for solving convex partially separable optimization problems. (English) Zbl 0751.90060
For the convex, partially separable nonlinear programming problem a dual program is developed based on the Fenchel duality theory. Duality theorems are proved, i.e. statements about solvability and optimality of the primal and dual program which avoid a duality gap. For completely and tridiagonally separable systems some conclusions and applications are discussed, in particular the computation of cubic and quadratic $$C^ 1$$- splines for interpolation or data smoothing, respectively. In these cases, the conjugate functions of the dual problem can be determined explicitely. Some numerical results are reported. Finally the author investigates briefly triagonal linear complementary and obstacle problems.

##### MSC:
 90C25 Convex programming 65D10 Numerical smoothing, curve fitting 90-08 Computational methods for problems pertaining to operations research and mathematical programming 65D05 Numerical interpolation 65K10 Numerical optimization and variational techniques 41A15 Spline approximation