Diffusions for global optimizations
SIAM Journal on Control and Optimization
Diffusion for global optimization in Rn
SIAM Journal on Control and Optimization
Stable barrier-projection and barrier-Newton methods in linear programming
Computational Optimization and Applications - Special issue dedicated to George Dantzig
Optimal Inequalities in Probability Theory: A Convex Optimization Approach
SIAM Journal on Optimization
Studies of the behavior of recursion for the pooling problem
ACM SIGMAP Bulletin
Ambiguous chance constrained problems and robust optimization
Mathematical Programming: Series A and B
Linearly Constrained Global Optimization and Stochastic Differential Equations
Journal of Global Optimization
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
A review of recent advances in global optimization
Journal of Global Optimization
Convergence analysis of a global optimization algorithm using stochastic differential equations
Journal of Global Optimization
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We propose a stochastic algorithm for the global optimization of chance constrained problems. We assume that the probability measure with which the constraints are evaluated is known only through its moments. The algorithm proceeds in two phases. In the first phase the probability distribution is (coarsely) discretized and solved to global optimality using a stochastic algorithm. We only assume that the stochastic algorithm exhibits a weak* convergence to a probability measure assigning all its mass to the discretized problem. A diffusion process is derived that has this convergence property. In the second phase, the discretization is improved by solving another nonlinear programming problem. It is shown that the algorithm converges to the solution of the original problem. We discuss the numerical performance of the algorithm and its application to process design.