#### Application of optimization techniques to PDEs (started in 2009)

Parabolic-type problems, involving a variational complementarity formulation, arise in mathematical models of several applications in Engineering, Economy, Biology and different branches of Physics. These kinds of problems present several analytical and numerical difficulties related, for example, to time evolution and a moving boundary. We develop numerical methods that employs a global convergent nonlinear complementarity (or mixed complementarity) algorithms for solving a discretized problem at each time step. Space discretization is implemented using the finite difference implicit scheme and the finite element method.

VIGO, D. G. A. ; CRUZ, A. A. ; CHAPIRO, G. ; GARCIA, G. C. ; MOREIRA, C. G. T. A. . Solving the inverse problem for an ordinary differential equation using conjugation. Journal of Computational Dynamics, v. 7, p. 183-208, 2020.

Gutierrez, A., Mazorche, S., R., Herskovits, J., Chapiro, G. An Interior Point Algorithm for Mixed Complementarity Nonlinear Problems, Journal of Optimization Theory and Applications, online, 1-18, 2017

Chapiro, G., Gutierrez, A., E., R., Herskovits, J., N., Mazorche, S., R., Pereira, W., S., Numerical Solution of a Class of Moving Boundary Problems with a Nonlinear Complementarity Approach. Journal of Optimization Theory and Applications, v. 168, p. 534-550, 2016.

Chapiro, G., Mazorche, S. R., Herskovits, J., Roche, J. R., Solution of the non-linear parabolic problems using nonlinear complementarity algorithm (fda-ncp). Mecánica Computacional, V. XXIX, P. 2141-2153, 2010.