On the normality of Lagrange multiplier rules for optimal control problems

Chapters in this book

1. Frontmatter 1
2. Preface 3
3. Contents 5
4. Invited Lectures
5. Saddle points and nonlinear differential equations 11
6. On optimal control problems described by operator equations in Banach and Hilbert spaces 19
7. Regularity results for some elliptic variational inequalities with bounded measurable coefficients and applications 29
8. Nonlinear equality constraints in optimization problems with set restrictions 41
9. On the speed of c₀-sequences in connection with a lemma of Toeplitz 53
10. On some optimal control problems for elliptic systems in the plane 65
11. On an initial-boundary value problem for the nonlinear Schrödinger equation with selfconsistent potential 75
12. On initial value problems in thermodynamics 89
13. Common properties of nonlinear programming algorithms basing on sequential unconstrained minimizations 107
14. The finite-difference method for a mildly nonlinear elliptic problem 119
15. Finite element analysis of the unilateral contact between elastic bodies 129
16. An inverse problem for "coefficients" in linear equations. Uniqueness and iterative solution 139
17. Nonlinear operators and solvability of operator equations 149
18. On convergence properties of families of maximal monotone operators 155
19. On perturbation of branching problems and secondary branching in the theory of plates 165
20. On a program for the computation of matter transport in river networks 181
21. Existence and regularity theorems for weak solutions to the equations of motion of visco-plastic media 189
22. A necessary and sufficient condition for the regularity of weak solutions to nonlinear elliptic systems of partial differential equations 201
23. Problems in connection with the Hahn-Banach Theorem 211
24. Parabolic problems with free boundaries: Existence and properties of solutions; optimal control problems 221
25. Optimization methods for non-linear partial differential equations 233
26. Design sensitivity analysis in structural mechanics 245
27. On optimal control problems in civil-engineering and technology 255
28. Das asymptotische Verhalten von Toeplitzdeterminanten für einige Klassen von Erzeugerfunktionen 267
29. Optimization and best approximation 273
30. Control in coefficients for PDE 287
31. Towards a general-purpose difference scheme for the linear one-dimensional parabolic equation 297
32. Two-component flow round a solid sphere 315
33. To the mathematical treatment of a technical heat control problem 327
34. Communications
35. On the radius of a set in a Hilbert space 337
36. On the variational method without coerciveness 339
37. Special control problems and monotone operators 343
38. A generalization of an optimality theorem 347
39. Mixed variational formulation of unilateral problems 351
40. Sufficient conditions for optimality of a control problem with discrete time 357
41. A controllability problem of nonlinear dynamical systems 361
42. On the convergence of the finite elements method for some initial problem 367
43. On the normality of Lagrange multiplier rules for optimal control problems 371
44. Some methods of solving optimal control problems for free boundary processes 375
45. Ein Approximations-Iterationsverfahren für nichtlineare Volterrasche Integralgleichungen zweiter Art 379
46. Secondary axisymmetric buckled states of thin elastic spherical shells 385
47. Perturbation and branching of the solutions of nonlinear eigenvalue problems 389
48. Zur Existenz der optimalen Steuerung bei Volterraschen Integralgleichungen 395
49. The finite difference method for quasilinear elliptic equations with rapidly increasing coefficients 399
50. A constructive proof of the implicit function theorem for analytic operators 403
51. Some remarks to existence problems of optimal control for parabolic equations 407
52. Construction of local solutions for Maxwell equations 413
53. An abstract equation modelling diffusion in solids with bidisperse pore structure 417
54. Bifurcation of axially compressed circular cylindrical shells with free edges 421
55. On difference approximations of a class of it-dimensional variational inequalities 427
56. On some Stefan like problem 433
57. On a system of nonlinear partial differential equations arising in the theory of heat and mass transfer in a nonlinear second-order fluid 437