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University of Florida

1. Zhao, Zinan. A New Scalable Paradigm for High-Dimensional Chance Constrained Programs.

Degree: PhD, Mechanical Engineering - Mechanical and Aerospace Engineering, 2015, University of Florida

A new paradigm for accurate transcription of chance constraints in a computationally scalable manner is presented for large-scale chance constrained programs. We first present an extension of the so-called Bernstein approximation by coupling it with Markov chain Monte Carlo (MCMC) integration for chance constrained optimization problems having nonlinear, nonconvex constraint functions and inter-dependent random variables. The Bernstein approximation replaces chance constraints with deterministic constraints and relies upon the evaluation of exponential moment generating functions that are typically high-dimensional integrals. This computationally burdensome task can be readily handled using MCMC integration, drawing upon MCMC's strength with high-dimensional integration. While the MCMC/Bernstein approach is computationally efficient, it can be overly conservative, whereby its solutions can be (severely) suboptimal. To reduce conservatism, manual tuning must be performed, which is ad-hoc at best and provides no guarantee of optimality. Advisors/Committee Members: KUMAR,MRINAL (committee chair), BAROOAH,PRABIR (committee member), HAGER,WILLIAM WARD (committee member).

Subjects/Keywords: Approximation; Constrained optimization; Design optimization; Linear programming; Optimal control; Random variables; Randomness; Simulations; Spacecraft; Textual collocation; optimalcontrol  – optimization

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Zhao, Z. (2015). A New Scalable Paradigm for High-Dimensional Chance Constrained Programs. (Doctoral Dissertation). University of Florida. Retrieved from http://ufdc.ufl.edu/UFE0047703

Chicago Manual of Style (16th Edition):

Zhao, Zinan. “A New Scalable Paradigm for High-Dimensional Chance Constrained Programs.” 2015. Doctoral Dissertation, University of Florida. Accessed October 20, 2019. http://ufdc.ufl.edu/UFE0047703.

MLA Handbook (7th Edition):

Zhao, Zinan. “A New Scalable Paradigm for High-Dimensional Chance Constrained Programs.” 2015. Web. 20 Oct 2019.

Vancouver:

Zhao Z. A New Scalable Paradigm for High-Dimensional Chance Constrained Programs. [Internet] [Doctoral dissertation]. University of Florida; 2015. [cited 2019 Oct 20]. Available from: http://ufdc.ufl.edu/UFE0047703.

Council of Science Editors:

Zhao Z. A New Scalable Paradigm for High-Dimensional Chance Constrained Programs. [Doctoral Dissertation]. University of Florida; 2015. Available from: http://ufdc.ufl.edu/UFE0047703

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