Abstract:
The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete components model phenomena such as fixed charges, dichotomies, piecewise linear functions, and general logical relationships between system entities. Nonlinearities are required to accurately represent phenomena such as covariance, economies of scale, and queuing delays, or physical properties such as pressure, stress, and equilibrium. Problems involving both discrete and nonlinear components are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems.
During the talk the theoretical foundations behind modern solution approaches to MINLP will be described. Discussion will center around building blocks such as relaxations, cutting planes, and search techniques that are all combined to build successful algorithms.