Novel line search procedure for very large scale optimisation

在这项工作中，我们感兴趣的一般优化模型的解决方案，包括一个非线性的目标函数和一般的非线性等式和不等式约束。特别感兴趣的是在工业和科学研究模型中出现的非常大规模的问题的解决方案，如最优控制问题，分子设计，蛋白质折叠和许多其他领域需要先进的解决方案。工程模型，特别是从过程建模中产生的模型，包含了很大比例的等式约束以及操作不等式约束和边界，封装在控制参数值和质量和可操作性满意度的限制。非线性优化领域在其存在的许多年里有许多令人鼓舞的想法，因此工程实践极大地受益于标准商业模拟包中的这种方法的可用性。这种方法涉及一种新的线搜索程序最初提出的主要研究者和同事，这是第一次提出了一个真正的非单调方面的目标和约束值。早期的结果表明，这样的属性允许优化求解器采取更少的步骤走向最佳点，甚至在某些情况下从局部极小值逃脱。

In this work we are interested in the solution of general optimisation models comprised of a nonlinear objective function and subject to general nonlinear equality and inequality constraints. Of particular interest is the solution of very large scale problems arising in industrial and scientific research models, such as optimal control problems, molecular design, protein folding and a host of other areas requiring the availability of advanced solvers. Engineering models, particularly ones arising from process modelling, contain a very large proportion of equality constraints as well as operational inequality constraints and bounds, encapsulating limits in control parameter values and quality and operability satisfaction. The field of nonlinear optimisation has enjoyed many inspiring ideas in its many years of existence, and engineering practice as a result has benefited greatly by the availability of such methods within standard commercial simulation packages.This proposal intends to develop further on a new concept for very large scale optimisation developed in our research group. This methodology involves a novel line search procedure proposed originally by the principal investigator and co-workers, which for the first time presents a true non-monotone aspect over both objective and constraint values. Early results indicate that such attributes allow the optimisation solver to take fewer steps towards an optimum point and even to escape from local minima in some cases.