Value Functions and Transversality Conditions for Infinite-Horizon Optimal Control Problems

This paper investigates the relationship between the maximum principle with an infinite horizon and dynamic programming and sheds new light upon the role of the transversality condition at infinity as necessary and sufficient conditions for optimality with or without convexity assumptions. We first derive the nonsmooth maximum principle and the adjoint inclusion for the value function as necessary conditions for optimality that exhibit the relationship between the maximum principle and dynamic programming. We then present sufficiency theorems that are consistent with the strengthened maximum principle, employing the adjoint inequalities for the Hamiltonian and the value function. Synthesizing these results, necessary and sufficient conditions for optimality are provided for the convex case. In particular, the role of the transversality conditions at infinity is clarified

A simple instrument for assessing stress in clinical practice.

Methods to assess the role of stress factors in patients with medical conditions are often rather complex, require specific training, and are difficult to use in clinical practice. We attempted to develop a short index tailored to a busy clinical setting, which would be easy to use while providing adequate individual information. This index (Psychosocial Index) was largely derived from well-established instruments, such as Kellner's Screening List for Psychosocial Problems. In addition, on the basis of the patient's self-report of items, the clinician is asked to rate four dimensions of the patient's life: stress, wellbeing, psychological distress, and illness behaviour. The questionnaires of 34 female patients with functional medical disorders were first rated by an internist and afterwards, blindly, by a psychiatrist. Agreement between the two raters was excellent, as measured by the intraclass correlation coefficient. It is hoped that this Psychosocial Index may provide a new tool for psychosomatic research and practice