Reduced order representation of robust multi-target multi-agent sensor allocation

Most of the prevailing optimization packages only accept a quadratic conic representation of a second order cone program. The algorithms that convert the Lorentz conic constraint to such a representation, dramatically increase the size of the original problem by adding new variables and constraints. This impairs the solver performance, particularly in the large-scale problems, where the memory availability is one of the main concerns. This paper proposes a novel conversion algorithm, to achieve a minimal representation as well as a reduced order scheme that substantially decreases the dimensions of the converted model while maintaining the properties of the original problem. The algorithm provides a convenient way to achieve a good compromise between the problem size and the level of approximation by a single parameter. The simulation results confirm the effectiveness of the conversion algorithm on some mixed integer second order cone program optimization problems arising in robust multi-agent multi-target sensor allocation applications. The conducted analyses indicate that while the desired robustness level is achieved, the problem size can be substantially reduced in exchange for negligible performance degradation.