1504. Second-Order Cone Programming in Measures using Polynomial Optimization
Invited abstract in session MA-49: Sums-of-squares optimization, stream Conic and polynomial optimization.
Monday, 8:30-10:00Room: Parkinson B10
Authors (first author is the speaker)
| 1. | Jared Miller
|
| 2. | Jie Wang
|
| Academy of Mathematics and Systems Science | |
| 3. | Matteo Tacchi
|
| GIPSA |
Abstract
Second order cone programs (SOCPs) are a fundamental tool in convex optimization. Applications of finite-dimensional SOCPs include stochastic linear programming, spectrum allocation, and robust linear-quadratic model predictive control. This work studies infinite-dimensional SOCPs posed over nonnegative Borel measures. The SOCP in measures involves a linear objective over a (possibly infinite) set of finite-dimensional second-order-cone and linear constraints. SOCPs in measures are present in the setting of infinite-dimensional quadratic programs in which all kernels possess known and finite-dimensional feature maps. We demonstrate that the SOCPs obey strong duality under compactness and continuity assumptions, and prove that the moment-sum-of-squares hierarchy of semidefinite programs will converge to the true SOCP optima under assumptions of polynomial structure. We apply this methodology towards solving measure SOCPs arising in risk analysis, optimal control with non-local quadratic costs, and design of periodic distributions.
Keywords
- Global Optimization
- Convex Optimization
- Mathematical Programming
Status: accepted
Back to the list of papers