A reduced subgradient algorithm. (English) Zbl 0624.90085

Bihain, A.; Nguyen, V. Hien; Strodiot, J.-J.

Math. Program. Study 30, 127-149 (1987).

The authors describe an iterative method for the approximate solution of nondifferentiable convex programming problems. The problems incorporate linear equality and inequality constraints \((Ax=b\), \(x\geq 0)\); the method combines Wolfe’s well-known reduced gradient algorithm with the bundle method of nonsmooth optimization. The algorithm is explained clearly, convergence is proved, and five numerical examples are presented.

Reviewer: P.Loewen

MSC:

90C25	Convex programming
65K05	Numerical mathematical programming methods
90C55	Methods of successive quadratic programming type

Keywords:

linearly constrained minimization; approximate solution; nondifferentiable convex programming; reduced gradient algorithm; bundle method; nonsmooth optimization