scholarly journals Necessary conditions for a mathematical programming problem with set and cone constraints

1988 ◽  
Vol 29 (3) ◽  
pp. 310-321
Author(s):  
Youji Nagahisa
Keyword(s):  
Mathematical Programming ◽  
Programming Problem ◽  
State Constraints ◽  
Necessary Conditions ◽  
Open Mapping ◽  
Necessary Condition ◽  
Mathematical Programming Problem ◽  
Open Mapping Theorem ◽  
Cone Constraints ◽  
Inequality State

AbstractThis paper is devoted to the derivation of a necessary condition of F. John type which must be satisfied by a solution of a mathematical programming problem with set and cone constraints. The necessary condition is applied to an optimisation problem defined on functional spaces with inequality state constraints. Furthermore a pseudo open mapping theorem is developed in the course of proving the main theorem.

scholarly journals Generalized convexity in nondifferentiable programming

1984 ◽  
Vol 30 (2) ◽  
pp. 193-218 ◽  
Author(s):  
Bevil M. Glover
Keyword(s):  
Mathematical Programming ◽  
Optimality Conditions ◽  
Programming Problem ◽  
Constraint Qualification ◽  
Generalized Convexity ◽  
Nondifferentiable Programming ◽  
Mathematical Programming Problem ◽  
Sufficient Optimality Conditions ◽  
Cone Constraints ◽  
Necessary And Sufficient

For an abstract mathematical programming problem involving quasidifferentiable cone-constraints we obtain necessary (and sufficient) optimality conditions of the Kuhn-Tucker type without recourse to a constraint qualification. This extends the known results to the non-differentiable setting. To obtain these results we derive several simple conditions connecting various concepts in generalized convexity not requiring differentiability of the functions involved.

Linear Quadratic Optimal Control Via Fourier-Based State Parameterization

1991 ◽  
Vol 113 (2) ◽  
pp. 206-215 ◽  
Author(s):  
V. Yen ◽  
M. Nagurka
Keyword(s):  
Optimal Control ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Quadratic Programming Problem ◽  
Necessary Condition ◽  
Mathematical Programming Problem ◽  
Linear Quadratic ◽  
Linear Algebraic Equations ◽  
Linearly Constrained ◽  
Lq Problem

A method for determining the optimal control of unconstrained and linearly constrained linear dynamic systems with quadratic performance indices is presented. The method is based on a modified Fourier series approximation of each state variable that converts the linear quadratic (LQ) problem into a mathematical programming problem. In particular, it is shown that an unconstrained LQ problem can be cast as an unconstrained quadratic programming problem where the necessary condition of optimality is derived as a system of linear algebraic equations. Furthermore, it is shown that a linearly constrained LQ problem can be converted into a general quadratic programming problem. Simulation studies for constrained LQ systems, including a bang-bang control problem, demonstrate that the approach is accurate. The results also indicate that in solving high order unconstrained LQ problems the approach is computationally more efficient and robust than standard methods.

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