The lagrange-newton method for infinite-dimensional optimization problems

This paper investigates local convergence properties of the Lagrange-Newton method for optimization problems in reflexive Banach spaces. Sufficient conditions for quadratic convergence of optimal solutions and Lagrange multipliers are given. The results are applied to optimal control problems.

[1]  Boris Polyak,et al.  Constrained minimization methods , 1966 .

[2]  M. Hestenes.  Calculus of variations and optimal control theory , 1966 .

[3]  J. P. Lasalle,et al.  functional analysis and time Optimal Control , 1969 .

[4]  Stephen M. Robinson,et al.  Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms , 1974, Math. Program..

[5]  Stephen M. Robinson,et al.  Regularity and Stability for Convex Multivalued Functions , 1976, Math. Oper. Res..

[6]  I. Ekeland,et al.  Convex analysis and variational problems , 1976 .

[7]  A. Ioffe,et al.  Theory of extremal problems , 1979 .

[8]  Stephen M. Robinson,et al.  Strongly Regular Generalized Equations , 1980, Math. Oper. Res..

[9]  H. Maurer.  First and second order sufficient optimality conditions in mathematical programming and optimal control , 1981 .

[10]  A. Dontchev.  Perturbations, Approximations, and Sensitivity Analysis of Optimal Control Systems , 1983 .

[11]  J. Stoer.  Principles of Sequential Quadratic Programming Methods for Solving Nonlinear Programs , 1985 .

[12]  Kazimierz Malanowski,et al.  Stability of solutions to convex problems of optimization , 1987 .

[13]  Kazimierz Malanowski,et al.  Stability and sensitivity of solutions to optimal control problems for systems with control appearing linearly , 1987 .

[14]  S. M. Robinson.  Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity , 1987 .

[15]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[16]  K. C. P. Machielsen,et al.  Numerical Solution of Optimal Control Problems with State Constraints by Sequential Quadratic Programming in Function Space. , 1993 .

[17]  Stability of solutions for a class of nonlinear cone constrained optimization problems, part 2: Application to parameter estimation , 1989 .

[18]  W. Alt.  Stability of solutions for a class of nonlinear cone constrained optimization problems, part 1: Basic theory , 1989 .