Variational problems and l 1 exact exponential penalty function with (p,r) (,)-invexity
Pubali Mandal, Bibhas Chandra Giri, Chandal Nahak · 2014
In this paper, we formulate variational problems and establish weak, strong and converse duality theorems to relate solutions of the primal and dual problems with new generalized (p,r) � (�,�)-invexity assumptions on the functions involved. We also study the sufficient conditions for optimality and provide some examples to illustrate our works. We transform the constrained variational problem into an unconstrained one with the help of l1 exact exponential penalty function method. The equivalence between sets of optimal solutions of the original variational problem and its associated exponential penalized variational problem is established with new type of generalized invexity assumptions.