Numerical Optimization :
In recent years there is a growing interest of developing new optimization algorithms and their application in science, engineering , economics and industry. Our main focus in this area is to develop some new numerical approximation algorithms for continuous optimization problems including single objective and multiobjective cases. Some of these algorithms are Newton like line search methods, where we approximate the hessian using various techniques. Since 2008 there is a demand for developing multi-objective numerical optimization techniques so that hurestic and scalarization approaches can be avoided and proper convergence property of the iteration process can be established. We use differenet penalty functions and develop some superlinear convergent algorithms for constrained vector optimization problems.
Optimization with Uncertainty:
Studying the existence of optimal solution of nonlinear programming problems in complex situations is one of the emerging research areas of both theoretical and applied mathematics. Complexity of the optimization problems increases in an uncertain environment. In fact most of the real life optimization models have uncertain parameters. The researchers, working in this area, usually consider these uncertain parameters as linguistic variables or random variables, for which sometimes, selection of membership function and distribution function becomes burden to the decision maker. Recently some researchers have realized that the uncertain parameters can be considered as intervals to overcome these difficulties . We see that since the set of intervals is not totally ordered so classical optimization techniques fail to address these situations. We are developing some modified optimization techniques for solving different types of complex nonlinear optimization problems with interval parameters.
Convex Optimization: Convexity plays an important in optimization theory. We have studied E-Convex and generalized E-Convex properties of continuous optimization problems with differentiability assumption.
- Co-Principal Investigator
Ph. D. Students
Bhuvnesh Khatana
Area of Research: Numerical linear algebra and applications
Dinesh Kumar
Area of Research: Numerical Optimization
Nantu Kumar Bisui
Area of Research: Numerical Optimization
Sarishti Singh
Area of Research: Numerical Optimization
