# Optimization Problems with Multiple Characteristics

We are working on real-world, large-scale, hard optimization problems that have
multiple, interesting problem characteristics. While they can be broadly grouped
under the category of mixed-integer nonlinear programming problems, the following
examples can exhibit any of the following problem components: discrete variables,
continuous variables, linear functions, nonlinear functions, cone constraints,
complementarity/equilibrium constraints.

## Portfolio Optimization Problems

These are examples of mixed-integer second-order cone programming problems arising in
portfolio optimization.

## Multivehicle Path Coordination under Communication Constraints

These are nonconvex nonlinear reformulations of mixed-integer programming problems
arising in the discretization of the multivehicle path coordination problem. The
paths are represented by cubic splines, and the vehicles are required to be in
communication with a given number of others at all times. The nonlinear models include
second-order cone constraints to limit distance between vehicles in communication
and complementarity constraints to ensure sufficient communication and arrival information.
We also considered a scenario with 10 vehicles and a moving jammer:
Model and Data

## Cell Manufacturing Problems with No Partial Leftover Lots

These are lot-sizing problems arising in manufacturing, where the lot-size left at
the end of a manufacturing cycle cannot be a partial lot. This requires the lot-sizes
to be a fraction (with integer denominator) or an integer multiple of the demand.
As such, these problems have integer variables and complementarity constraints.

The development of this page and all posted materials was supported by
NSF Grant CCF-0725692. Other materials are available here
and here.