Informatica

One of the most known applications of Discrete Optimization is on scheduling. In contrast, one of the most known applications of Continuous Nonlinear Optimization is on the control of dynamic systems. In this paper, we combine both views, solving scheduling problems as dynamic systems, modeled as discrete-time nonlinear optimal control problems with state and control continuous variables subjected to upper and lower bounds. Complementarity constraints are used to represent scheduling decisions. One example we discuss in detail is the crude oil scheduling in ports, with numerical results presented.

Error bounds are developed for a class of quadratic programming problems. The absolute error between an approximate feasible solution, generated via a dual formulation, and the true optimal solution is measured. Furthermore, these error bounds involve considerably less work computationally than existing estimates.