Numerical methods, simulations and applications (174030)

Head of the project: Nataša Krejić, PhD

Duration of the project: 2011-2020

The nonlinearity of mathematical models arising in almost all scientific areas, from social sciences and economics to engineering and medicine, implies that closed-form solutions do not exist and a numerical approach is necessary. Simulation techniques play a pivotal role in model development, and numerical solution of uncertainty or noise is present, as is the case with many applications. The applicability of numerical methods and simulations is thus the main force driving the rich mathematical area, with research efforts concentrated both on theoretical challenges and computational implementation. Our research efforts will focus on numerical optimization and numerical methods for singularly perturbed problems. Within numerical methods for continuous optimization, we will consider the following topics: Continuos optimization problems of large scale; Nonsmooth problems with the non-smoothness present in the objective function and constraints; Continuos optimization problems in a noisy environment; Variable sample size methods; Optimization models in algorithmic trading; Optimization problems in medicine - cluster analysis. The planned research within the second research direction includes one-dimensional and two-dimensional problems with one or more perturbation parameters. The objective will be to derive and analyze robust numerical methods on layer-adapted meshes resulting in uniform convergence.