Enhanced Fritz John Optimality Conditions

2011 ◽  
pp. 225-260
Keyword(s):  
Optimality Conditions ◽  
Fritz John Optimality Conditions

scholarly journals Sufficient Fritz John optimality conditions for nondifferentiable convex programming

1976 ◽  
Vol 19 (4) ◽  
pp. 462-468 ◽  
Author(s):  
B. D. Craven ◽  
B. Mond
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Programming Problem ◽  
Convex Programming ◽  
Necessary Conditions ◽  
Nonlinear Programming Problem ◽  
Necessary Conditions For Optimality ◽  
Ordered Space ◽  
Sufficiency Theorem ◽  
Fritz John Optimality Conditions

AbstractThe Fritz John necessary conditions for optimality of a differentiable nonlinear programming problem have been shown, given additional convexity hypotheses, to be also sufficient (by Gulati, Craven, and others). This sufficiency theorem is now extended to minimization (suitably defined) of a function taking values in a partially ordered space, and to (convex) objective and constraint functions which are not always differentiable. The results are expressed in terms of subgradients.

Sufficient Fritz John optimality conditions

1975 ◽  
Vol 13 (3) ◽  
pp. 411-419 ◽  
Author(s):  
B.D. Craven
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Linear Subspace ◽  
Arbitrary Dimension ◽  
Differentiable Manifold ◽  
The Other ◽  
Sufficient Optimality Conditions ◽  
Polyhedral Cones ◽  
Finite Dimensional ◽  
Fritz John Optimality Conditions

The sufficient optimality conditions, of Fritz John type, given by Gulati for finite-dimensional nonlinear programming problems involving polyhedral cones, are extended to problems with arbitrary cones and spaces of arbitrary dimension, whether real or complex. Convexity restrictions on the function giving the equality constraint can be avoided by applying a modified notion of convexity to the other functions in the problem. This approach regards the problem as optimizing on a differentiable manifold, and transforms the problem to a locally equivalent one where the optimization is on a linear subspace.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

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