Optimization and Electronic Structure Calculations
J. M. Martinez

Ab initio electronic structure calculations provide a number of interesting optimization problems, from unconstrained minimization to nonlinear systems of equations and nonlinear programming.  In this talk we focus on three optimization problems with decreasing generality.  The more general problem is the smooth nonconvex nonlinear minimization problem with constraints and the more specific one is the optimization problem vinculated to the Restricted Hartree Fock Closed Shell equations.

Based on these problems the notions of global and local minimizers and stationary points are revisited and the concept of Aufbau point is defined for general optimization.  The basic fixed point algorithm that seeks Aufbau points is analyzed and the alternatives for its globalization are discussed.  This talk will be based on joint research with Juliano B. Francisco and Leandro Martinez.