Numerical Method For Heat Transfer Under Chance Constrained State Variables

Stochastic chance-constrained programming is mainly concerned with the problem thatrnthe decision maker must give his solution before the random variables come true. Inrnthis problem, the probability of decision satisfying the constraints cannot be less thanrnsome given probability level, or reliability level or con dence level . There are two mainrndi culties with such chance-constrained problems. First, checking feasibility of a givenrncandidate solution exactly is impossible in general. Second, the feasible region inducedrnby chance constraints is, in general, non-convex leading to severe optimization challenges.rnChance constrained optimization problems in engineering applications possess highlyrnnon-linear process models and non-convex structures. As a result, solving a non-linearrnnon-convex chance constrained optimization (CCOPT) problem remains as a challengingrntask. The major di culty lies in the evaluation of probability values and gradients ofrninequality constraints which are non-linear functions of stochastic variables. This thesisrnwill focus on Inner-Outer smooth analytic approximation to improve tractability ofrnnon-convex chance constraints. Also this thesis is devoted to an example of optimizationrnproblems that include PDEs constraint in the case of heat transfer by implementing thernInner-Outer approximation scheme.

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