scholarly journals Optimality conditions for systems with insufficient data

1990 ◽  
Vol 41 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
A Priori ◽  
Sufficient Conditions ◽  
Distributed Parameter ◽  
Not Given ◽  
Cost Criterion ◽  
Distributed Parameter Control ◽  
Recent Theorem ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient ◽  
Distributed Parameter Control System

In this paper we use the Dubovitski–Milyutin formalism to establish necessary and sufficient conditions for optimality in a nonlinear, distributed parameter control system, with convex cost criterion and initial condition not given a priori (that is it is not a known function but instead it belongs to a specified set). Our result extends a recent theorem of Lions. Finally a concrete example is worked out in detail.

scholarly journals Invexity of supremum and infimum functions

2002 ◽  
Vol 65 (2) ◽  
pp. 289-306 ◽  
Author(s):  
Nguyen Xuan Ha ◽  
Do Van Luu
Keyword(s):  
Sufficient Conditions ◽  
Infinite Family ◽  
Lipschitz Functions ◽  
Necessary And Sufficient Conditions ◽  
Directional Derivatives ◽  
Mathematical Programs ◽  
Sufficient Conditions For Optimality ◽  
Invex Function ◽  
Necessary And Sufficient

Under suitable assumptions we establish the formulas for calculating generalised gradients and generalised directional derivatives in the Clarke sense of the supremum and the infimum of an infinite family of Lipschitz functions. From these results we derive the results ensuring such a supremum or infimum are an invex function when all functions of the invex. Applying these results to a class of mathematical programs, we obtain necessary and sufficient conditions for optimality.

scholarly journals An inverse spectral problem for Sturm-Liouville-type integro-differential operators with robin boundary conditions

2019 ◽  
Vol 50 (3) ◽  
pp. 207-221 ◽  
Author(s):  
Sergey Buterin
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Boundary Conditions ◽  
Differential Operators ◽  
A Priori ◽  
Sufficient Conditions ◽  
Robin Boundary Conditions ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
Robin Boundary

The perturbation of the Sturm--Liouville differential operator on a finite interval with Robin boundary conditions by a convolution operator is considered. The inverse problem of recovering the convolution term along with one boundary condition from the spectrum is studied, provided that the Sturm--Liouville potential as well as the other boundary condition are known a priori. The uniqueness of solution for this inverse problem is established along with necessary and sufficient conditions for its solvability. The proof is constructive and gives an algorithm for solving the inverse problem.

Generalized semi-Markov decision processes

1979 ◽  
Vol 16 (03) ◽  
pp. 618-630
Author(s):  
Bharat T. Doshi
Keyword(s):  
Markov Decision Processes ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
The State ◽  
Service Rate ◽  
Storage Model ◽  
Sample Paths ◽  
Markov Decision ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient

Various authors have derived the necessary and sufficient conditions for optimality in semi-Markov decision processes in which the state remains constant between jumps. In this paper similar results are presented for a generalized semi-Markov decision process in which the state varies between jumps according to a Markov process with continuous sample paths. These results are specialized to a general storage model and an application to the service rate control in a GI/G/1 queue is indicated.

scholarly journals Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ismail Kucuk ◽  
Kenan Yildirim
Keyword(s):  
Maximum Principle ◽  
Space Dimension ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Distributed Parameter ◽  
Hyperbolic Partial Differential Equation ◽  
The Maximum Principle ◽  
Convexity Assumptions ◽  
Necessary And Sufficient ◽  
One Space Dimension

The present paper deals with the necessary optimality condition for a class of distributed parameter systems in which the system is modeled in one-space dimension by a hyperbolic partial differential equation subject to the damping and mixed constraints on state and controls. Pontryagin maximum principle is derived to be a necessary condition for the controls of such systems to be optimal. With the aid of some convexity assumptions on the constraint functions, it is obtained that the maximum principle is also a sufficient condition for the optimality.

NECESSARY AND SUFFICIENT CONDITIONS FOR DYNAMIC OPTIMIZATION

2014 ◽  
Vol 20 (3) ◽  
pp. 667-684 ◽  
Author(s):  
A. Kerem Coşar ◽  
Edward J. Green
Keyword(s):  
Optimization Problems ◽  
Infinite Horizon ◽  
Sufficient Conditions ◽  
Transversality Condition ◽  
Necessary And Sufficient Conditions ◽  
Infinite Horizon Optimization ◽  
Sufficient Conditions For Optimality ◽  
The Government ◽  
Duality Approach ◽  
Necessary And Sufficient

We characterize the necessary and sufficient conditions for optimality in discrete-time, infinite-horizon optimization problems with a state space of finite or infinite dimension. It is well known that the challenging task in this problem is to prove the necessity of the transversality condition. To do this, we follow a duality approach in an abstract linear space. Our proof resembles that of Kamihigashi (2003), but does not explicitly use results from real analysis. As an application, we formalize Sims's argument that the no-Ponzi constraint on the government budget follows from the necessity of the tranversality condition for optimal consumption.

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