Second Order Sufficient Optimality Conditions for Some State-constrained Control Problems of Semilinear Elliptic Equations

This paper deals with a class of optimal control problems governed by elliptic equations with nonlinear boundary condition. The case of boundary control is studied. Pointwise constraints on the control and certain equality and set-constraints on the state are considered. Second order sufficient conditions for local optimality of controls are established.

[1]  N. Josephy.  Newton's Method for Generalized Equations. , 1979 .

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

[3]  E. Casas.  Boundary control of semilinear elliptic equations with pointwise state constraints , 1993 .

[4]  H. Goldberg,et al.  Second-order sufficient optimality conditions for a class of nonlinear parabolic boundary control problems , 1993 .

[5]  W. Hager,et al.  Optimality, stability, and convergence in nonlinear control , 1995 .

[6]  J. Zowe,et al.  Second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems , 1979 .

[7]  E. Casas,et al.  Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semiline , 1996 .

[8]  W. Alt.  The lagrange-newton method for infinite-dimensional optimization problems , 1990 .

[9]  S. M. Robinson.  Stability Theory for Systems of Inequalities. Part I: Linear Systems , 1975 .

[10]  G. Stampacchia,et al.  Inverse Problem for a Curved Quantum Guide , 2012, Int. J. Math. Math. Sci..

[11]  G. Stampacchia,et al.  Problemi al contorno ellittici, con dati discontinui, dotati di soluzioni hölderiane , 1960 .

[12]  J. Zowe,et al.  Regularity and stability for the mathematical programming problem in Banach spaces , 1979 .

[13]  G. Stampacchia,et al.  A variational inequality with mixed boundary conditions , 1972 .

[14]  Fredi Tröltzsch,et al.  Second Order Sufficient Optimality Conditions for a Nonlinear Elliptic Boundary Control Problem , 1996 .

[15]  A. Ioffe.  Necessary and Sufficient Conditions for a Local Minimum. 3: Second Order Conditions and Augmented Duality , 1979 .

[16]  J. F. Bonnans,et al.  Second-Order Analysis for Control Constrained Optimal Control Problems of Semilinear Elliptic Systems , 1998 .

[17]  F. Tröltzsch,et al.  Second order optimality conditions for a class of control problems governed by non-linear integral equations with application to parabolic boundary control , 1989 .

[18]  W. Alt.  On the approximation of infinite optimization problems with an application to optimal control problems , 1984 .

[19]  Fredi Tröltzsch.  Optimality conditions for parabolic control problems and applications , 1984 .