Advised by Lorenz T. Biegler
Process engineering encompasses a wide variety of problems exhibiting continuous, discontinuous switching or discrete behavior. This behavior may result in change in equations governing the system and typically result in a nonsmooth problem. Some characteristic examples include phase changes in equilibrium systems, changes in operational modes of safety and relief valves, overflowing of tanks or discrete decisions made by controls. Such systems are termed hybrid and have been largely modeled using binary variables. In this work, we employ complementarity constraints to model these systems resulting a smooth formulation. The smooth formulation allows us to employ standard nonlinear programing algorithms for the solution of these models.
Complementarity constraints have largely been avoided in the modeling community due to the violation of standard regularity of the resulting formulation. This needs to be revisited in the face of recent work on MPCCs. A number of existing algorithms have been shown to work well on MPCCs with good convergence behavior. In particular, we have shown that Interior Point algorithms for nonlinear programs can be easily adapted for the solution of MPCCs. We have incorporated our ideas into such an algorithm, IPOPT and have shown good pratical behavior on a number of process engineering problems.
In this talk, we will focus on the formulation of bilevel programming probelms and piecewise smooth systems using complementarity constraints. We will present results from using our formulation to solve dynamic problems namely, metabolic engineering problems and dynamic distillation columns with phases changes. The metabolic engineering problem is a dynamic parameter estimation with an inner optimization problem that needs to be solved at each time step. The distillation column is posed as an optimal control problem, aiming to minimize the start-up time.