Abebaw Tilahun (PhD)Sani MohammedAmare Getinet2019-04-252023-11-042019-04-252023-11-042017-11-06http://etd.aau.edu.et/handle/123456789/18147Stochastic 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.enStochastic Optimal ControlProbability ConstraintChance constrained optimization and Analytic approximationThesis