123260238
Some Clarifications on the Transversality Condition
In this paper, the authors study a general concave discrete-time, infinite-horizon, optimal-control problem. They establish necessary and sufficient conditions for optimality in the weak sense of W. A. Brock and for optimality in the strong sense of D. Gale. The corresponding transversality conditions are general exhaustion properties of the limit value of the optimal state variables; these properties cover and extend the well-known results obtained in special cases. Copyright 1990 by The Econometric Society.
120249515
Necessary Conditions for Optimality of Elliptic Systems with Positivity Constraints on the State
Recently, necessary conditions for optimality were established in the case of nonlinear elliptic multi-dimensional systems with integral constraints [P. Michel, Condition necessaire d’optimalite pour des systemes d’equations elliptiques non lineaires, Quatriemes journees de controle (Metz, 18–21 Mai 1976), polycopie Universite de Metz, 1976]. Here this problem is solved in the case of additional constraints of positivity of the state’s components on measurable sets.
126259170
Pour une extension du principe du maximum de Pontrjagin
16503488
On the Transversality Condition in Infinite Horizon Optimal Problems
121655740
Generalized controls: A necessary condition for optimality in a Banach space
Abstract A necessary condition is established for optimality in the case of problems where the constraints are simultaneously functions of the trajectory and the control (Problem 3.1, Theorem 5.7); this condition holds for generalized controls with values in a Hausdorff space and for a state space which is a Banach space. To demonstrate the result a new technique is used, based on the differentiability of the trajectory (Theorem 2.6) and the introduction of the notion of pseudosolution (Definition 2.8). These results are then applied to calculus of variations problems in a Banach space (Theorem 6.3).
179551139
Stricte ergodicite d’ensembles minimaux de substitution
On se propose de donner une demonstration de la stricte ergodicite des ensembles minimaux engendres par les substitutions de longueur non constante.
203998674
Average rank of families of elliptic curves and Sato-Tate laws