Research Projects

Reserachers introduce a penalty function of new kind for the problem (P) min x∈C f(x); (1) for a closed convex subset C in a Hilbert space H and f is a twice continuous Frechet differen- tiable on H. Under certain conditions, we will study the relations between problem (P) and its unconstrained reformulation in H: The main purpose of our investigation is to establish the depth layer of those properties of the objective function, which can be extended from feasible set to H concerning to P (penalty function). As a byproduct, we deliver some results on ”Approxima- tion and Optimization,” an emerging area of applied functional analysis in the current research scenario. The approximation theory deals with the approximation of the functions of a certain kind (for e.g. continuous function on some interval) by other probably simpler functions (for e.g. polynomials), such situation already arises in calculus; if a function has a Taylor series expansion, we may regard the partial sums of series as an approximation.