Triloki Nath

• Ph.D., Banaras Hindu University, Varanasi-INDIA
• Professor (Associate) at Deen Dayal Upadhyaya Gorakhpur University

(To appear in The Journal of Analysis) We establish a necessary and sufficient condition for the differentiability of the distance function generated by a nonempty closed set K in a real normed linear space X under a proximinality condition on K. We do not assume the uniform differentiability constraints on the norm of the space as in Giles [16]. H...

The power rule of differentiation has the power to provide simple proofs of numerous important results in Mathematics, Statistics, Engineering, and Economics. Motivated by Tao [4], we found an elementary proof of the power rule of differentiation for any real index. Our approach is elementary in the sense that we do not use product rule, quotient r...

In this paper, we use the concept of convexificators to derive enhanced Fritz John optimality condition for nonsmooth optimization problems having equality, inequality and abstract set constraint, where involved functions admit convexificators. This necessary optimality condition provides some more information about the extremal point in terms of c...

In this note, we remark, with sufficient mathematical rigor, that many weak generalizations of the usual minimum available in the literature are not true generalizations. Motivated by the Ekeland Variational Principle, we provide, first time, the criteria for weaker generalizations of the usual minimum. Further, we show that the quasi efficiency, r...

In this paper, we considered the mathematical programs with vanishing constraints or MPVC. We proved that an MPVC-tailored penalty function, introduced in [5], is still exact under a very weak and new constraint qualification. Most importantly, this constraint qualification is shown to be strictly stronger than MPVC-Abadie constraint qualification.

In this paper, we study the difficult class of optimization problems called the mathematical programs with vanishing constraints or MPVC. Extensive research has been done for MPVC regarding stationary conditions and constraint qualifications using geometric approaches. We use the Fritz John approach for MPVC to derive the M-stationary conditions un...

In this paper, we establish Lagrange multiplier rules in terms of Michel-Penot subdifferential for nonsmooth vector optimization problem. A constraint qualification or regularity condition in terms of Michel-Penot subdifferential is given and under this regularity condition the boundedness of certain sets of Lagrange multipliers are discussed.

In this paper, we investigate some properties of Michel Penot subdifferentials of locally Lipschitz functions and establish Lagrange multiplier rule in terms of Michel-Penot subdifferentials for nonsmooth mathematical programming problem.

We establish some relationships between vector variational-like inequality problems and nonsmooth vector optimization problems under the restriction that function is locally Lipschitz α-invex, acting between infinite dimensional spaces. We investigate the weakly efficient points, vector critical points and the solution of the non-smooth weak vector...