Joint Chance Constrained Programming: A Gradient Perspective
DescriptionJoint chance constrained programs (CCPs) are a class of challenging optimizationproblems. In this project, we study solution methods for joint CCPs that rely on MonteCarlo simulation, and focus on the sample average approximation approach to jointCCPs. Motivated by the recent advances on sensitivity estimation of expectations withdiscontinuous integrands in the simulation society, we introduce simulation methods forestimating gradients of the joint chance constraints, including a kernel smoothingmethod, and a conditional Monte Carlo (CMC) method. The kernel smoothing methodhandles joint chance constraints by extending the existing result on a singlediscontinuity point to multiple discontinuity points. The CMC method is generalized froma change-of-variables viewpoint that leads to new gradient estimators for joint chanceconstraints.We propose to incorporate the gradient estimators into gradient-based optimizationalgorithms to solve joint CCPs, which is an underdeveloped research area to our bestknowledge. We plan to study the theoretical foundations, algorithm design, andimplementation issues of such gradient-based optimization algorithms. It is expectedthat the outcomes of this project may contribute to the simulation and optimizationsocieties by adding efficient computational tools for solving joint CCPs.
|Effective start/end date||1/01/17 → 23/12/19|
- Chance constrained programs , Monte Carlo simulation , gradient estimation , sample average approximation ,