Dual algorithms for solving convex partially separable optimization problems. (English) Zbl 0751.90060

Schmidt, Jochen W.

Jahresber. Dtsch. Math.-Ver. 94, No. 1, 40-62 (1992).

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.

Reviewer: K.Schittkowski (Bayreuth)

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

Keywords:

convex, partially separable nonlinear programming; duality; quadratic \(C^ 1\)-splines; triagonal linear complementary