Numerical Method for Heat Transfer under Chance Constrained State Variables
No Thumbnail Available
Date
2017-11-06
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Addis Ababa University
Abstract
Stochastic chance-constrained programming is mainly concerned with the problem that
the decision maker must give his solution before the random variables come true. In
this problem, the probability of decision satisfying the constraints cannot be less than
some given probability level, or reliability level or con dence level . There are two main
di culties with such chance-constrained problems. First, checking feasibility of a given
candidate solution exactly is impossible in general. Second, the feasible region induced
by chance constraints is, in general, non-convex leading to severe optimization challenges.
Chance constrained optimization problems in engineering applications possess highly
non-linear process models and non-convex structures. As a result, solving a non-linear
non-convex chance constrained optimization (CCOPT) problem remains as a challenging
task. The major di culty lies in the evaluation of probability values and gradients of
inequality constraints which are non-linear functions of stochastic variables. This thesis
will focus on Inner-Outer smooth analytic approximation to improve tractability of
non-convex chance constraints. Also this thesis is devoted to an example of optimization
problems that include PDEs constraint in the case of heat transfer by implementing the
Inner-Outer approximation scheme.
Description
Keywords
Stochastic Optimal Control, Probability Constraint, Chance constrained optimization and Analytic approximation