Well-posedness for generalized mixed vector variational-like inequality problems in Banach space

In this article, we focus to study about well-posedness of a generalized mixed vector variational-like inequality and optimization problems with aforesaid inequality as constraint. We establish the metric characterization of well-posedness in terms of approximate solution set.Thereafter, we prove the sufficient conditions of generalized well-posedness by assuming the boundedness of approximate solution set. We also prove that the well-posedness of considered optimization problems is closely related to that of generalized mixed vector variational-like inequality problems. Moreover, we present some examples to investigate the results established in this paper

Relations between multidimensional interval-valued variational problems and variational inequalities

summary:In this paper, we introduce a new class of variational inequality with its weak and split forms to obtain an $LU$-optimal solution to the multi-dimensional interval-valued variational problem, which is a wider class of interval-valued programming problem in operations research. Using the concept of (strict) $LU$-convexity over the involved interval-valued functionals, we establish equivalence relationships between the solutions of variational inequalities and the (strong) $LU$-optimal solutions of the multi-dimensional interval-valued variational problem. In addition, some applications are constructed to illustrate the established results

Well-posedness for generalized mixed vector variational-like inequality problems in Banach space

In this article, we focus to study about well-posedness of a generalized mixed vector variational-like inequality and optimization problems with aforesaid inequality as constraint. We establish the metric characterization of well-posedness in terms of approximate solution set.Thereafter, we prove the sufficient conditions of generalized well-posedness by assuming the boundedness of approximate solution set. We also prove that the well-posedness of considered optimization problems is closely related to that of generalized mixed vector variational-like inequality problems. Moreover, we present some examples to investigate the results established in this paper

On nonsmooth multiobjective fractional programming problems involving (p, r)− ρ −(η ,θ)- invex functions

A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of (p,r)−ρ −(η,θ)-invex class about the Clarke generalized gradient. Under the above invexity assumption, sufficient conditions for optimality are given. Finally, three types of dual problems corresponding to (MFP) are formulated, and appropriate dual theorems are proved

A mathematical model on Acquired Immunodeficiency Syndrome

AbstractA mathematical model SEIA (susceptible-exposed-infectious-AIDS infected) with vertical transmission of AIDS epidemic is formulated. AIDS is one of the largest health problems, the world is currently facing. Even with anti-retroviral therapies (ART), many resource-constrained countries are unable to meet the treatment needs of their infected populations. We consider a function of number of AIDS cases in a community with an inverse relation. A stated theorem with proof and an example to illustrate it, is given to find the equilibrium points of the model. The disease-free equilibrium of the model is investigated by finding next generation matrix and basic reproduction number R0 of the model. The disease-free equilibrium of the AIDS model system is locally asymptotically stable if R0⩽1 and unstable if R0>1. Finally, numerical simulations are presented to illustrate the results

Minmax fractional programming problem involving generalized convex functions

In the present study we focus our attention on a minmax fractional programming problem and its second order dual problem. Duality results are obtained for the considered dual problem under the assumptions of second order $\left( {F,\alpha ,\rho ,d}\right)$ -type I functions

An exact minimax penalty function approach to solve multitime variational problems

This paper aims to examine an appropriateness of the exact minimax penalty function method applied to solve the partial differential inequation (PDI) and partial differential equation (PDE) constrained multitime variational problems. The criteria for equivalence between the optimal solutions of a multitime variational problem with PDI and PDE constraints and its associated unconstrained penalized multitime variational problem is studied in this work. We also present some examples to validate the results derived in the paper