Feasible Point Optimization Methods for Design and Other Engineering Applications

优化问题渗透到人类奋进的所有领域。 这些问题通常包括要最小化或最大化的目标函数（成本、利润、精度、重量、时间、燃料、耐久性等）。但要满足某些限制条件。除了最简单的情况，有效地解决这些问题需要使用“数值”优化工具。本赠款提供资金用于开发，分析，实施和测试数值算法，用于解决具有大量不等式约束的约束优化问题。这些问题在工程应用中很常见。算法寻求表现出强的理论收敛性能以及高的实际效率。 注意力集中在享受“可行性”和“单调下降”的算法上;即，构造一系列迭代（越来越好的解的估计），具有以下性质：（i）所有迭代满足不等式约束，（ii）目标函数值从迭代到迭代单调提高。可行性和单调下降在广泛的应用领域中具有价值。 特别是，在PI以前开发和实现算法的工作的背景下，这些属性已经受到了癌症研究，化学工程，集成电路设计，放射学等领域的用户的好评。此外，具有非常大量的不等式约束的问题在工程和科学的许多应用中是常见的。 因此，可以预期，与PI小组开发的先前算法和软件的情况一样，如果成功的话，从拟议研究中得出的算法和软件将在广泛的应用领域产生重大影响。

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.