Global convergence for Newton methods in mathematical programming
In constrained optimization problems in mathematical programming, one wants to minimize a functionalf(x) over a given setC. If, at an approximate solutionx n , one replacesf(x) by its Taylor series expansion through quadratic terms atx n and denotes byx n+1 the minimizing point for this overC, one has a direct analogue of Newton's method. The local convergence of this has been previously analyzed; here, we give global convergence results for this and the similar algorithm in which the constraint setC is also linearized at each step.
KeywordsNewton Method Global Convergence Local Convergence Constraint Qualification Quadratic Convergence
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