Set Squeezing Procedure for Quadratically Perturbed Chance-Constrained Programming

The set squeezing procedure, a new optimization methodology for solving chance-constrained programming problems under continuous uncertainty distribution, is proposed in this paper. The generally intractable chance constraints and unknown convexity are tackled by a novel analyses of local structure of the feasible set. Based on the newly discovered structure, it is proved that the set squeezing procedure converges and local optimality is guaranteed under mild conditions. Furthermore, efficient algorithms are derived for the set squeezing procedure under the widely used quadratically perturbed constraints. The developed method is applied to the mean squared error (MSE) based probabilistic transceiver design as an application example. Simulation results show that the MSE outage probability can be controlled tightly, which leads to lower transmit power, compared to the existing dominant safe approximation method and the bounded robust optimization method.

Automated summary

The paper introduces a new optimization methodology, called the set squeezing procedure, for solving chance-constrained programming problems under continuous uncertainty distribution. Through novel analyses of the local structure of the feasible set, the generally intractable chance constraints and unknown convexity are addressed. The set squeezing procedure is proved to converge and local optimality is guaranteed under mild conditions, with efficient algorithms derived for widely used quadratically perturbed constraints.