NEWTONS METHOD FOR OPTIMIZATION PROBLEMS WITH EQUALITY CONSTRAINTS

Let X be a normed linear space and let f, delta //1, . . . , delta //m be functionals defined on X. . The theory of Newton's method developed previously by the author is extended to the problem: Minimize f(x) subject to delta //i(x) equals 0, i equals 1, . . . , m. A generalized form of Newton's method which approximates a solution of this problem by a sequence of the form x//n// plus //1 equals x//n minus GAMMA //nP//n(x//n), where n equals 0, 1, 2, . . . , is presented.