| Author: | Liang, Fengjie |
| Title: | Data-driven distributionally robust chance-constrained linear matrix inequalities |
| Advisors: | Pan, Kai (LMS) |
| Degree: | M.Phil. |
| Year: | 2024 |
| Subject: | Matrix inequalities Control theory Semidefinite programming Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Logistics and Maritime Studies |
| Pages: | iii, 48 pages |
| Language: | English |
| Abstract: | In this thesis, we present approximation and reformulation techniques for problem with distributionally robust chance-constrained linear matrix inequality (DRCCLMI), aiming at overcoming the computational challenges posed by multidimensional integration and nonconvexity of feasible sets. DRCCLMI seek a robust solution which guarantees that the chance constraints are fulfilled for a wide range of possible distribution within an ambiguity set. Specifically, we consider a data-driven ambiguity set which includes all the potential distributions sharing the same moment information. We first propose an inner approximation for DRCCLMI in a general form to deal with common constraint structures encountered in real-world scenarios. The key method we use for approximation is the Conditional Value-at-Risk (CVaR) approach, which enables us to approximate DRCCLMI in a way that ensures a certain level of solution quality while maintaining the robustness of the original constraint. Second, we derive an inner approximation and exact reformulations for a special case of DRCCLMI with and without support information, respectively. Specifically, this special case refers to the situation where a block matrix structure is inherent in the linear matrix inequality. Notably, our approximation and reformulation techniques facilitate the transformation of the original DRCCLMI into a more tractable semidefinite programming (SDP) problem, simplifying the computational process and improving the accuracy and efficiency of the solution. The practicality and effectiveness of these techniques are demonstrated through numerical studies on two real-world applications: truss topology design problem and calibration problem. |
| Rights: | All rights reserved |
| Access: | open access |
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