Feasible Point Optimization Methods for Design and Other Engineering Applications

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Optimization problems pervade all areas of human endeavor. Such problems generally include an objective function to be minimized or maximized (cost, profit, accuracy, weight, time, fuel, durability, etc.) subject to satisfaction of certain constraints. In all but the simplest cases, effectively tackling these problems requires the use of "numerical" optimization tools. The present grant provides funding for developing, analyzing, implementing, and testing numerical algorithms for the solution of constrained optimization problems with a large number of inequality constraints. Such problems are common in engineering applications. Algorithms are sought that exhibit strong theoretical convergence properties as well as high practical efficiency. Attention is focused on algorithms that enjoy feasibility" and "monotone descent"; i.e., that construct a sequence of iterates (increasingly better estimates of the solution) with the property that (i) all iterates satisfy the inequality constraints, and (ii) the objective function value improves monotonically from iteration to iteration.Feasibility and monotone descent are of value in a broad range of application areas. In particular, in the context of the PI's previous work on developing and implementing algorithms, such properties have been acclaimed by users in areas ranging from cancer research to chemical engineering, to design of integrated circuits, to radiology, to mention but a few. Further, problems with a very large number of inequality constraints are common in many applications ranging over engineering and the sciences. Accordingly, it is anticipated that, as has been the case with previous algorithms and software developed by the PI's group, the algorithms and software that will come out of the proposed research if it is successful, will have a significant impact in a wide range of application areas.