Novel line search procedure for very large scale optimisation

在这项工作中，我们感兴趣的是解决由非线性目标函数组成的一般优化模型，并受一般非线性等式和不等式约束。特别感兴趣的是解决工业和科学研究模型中出现的大规模问题，例如最优控制问题，分子设计，蛋白质折叠和许多其他需要先进求解器的领域。工程模型，特别是由过程建模产生的模型，包含了相当大比例的等式约束以及操作不等式约束和边界，封装了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多年的存在中享受了许多鼓舞人心的想法，因此工程实践从标准商业模拟软件包中的这些方法的可用性中受益匪浅。本提案旨在进一步发展我们研究小组开发的非常大规模优化的新概念。该方法涉及一种新颖的线搜索程序，最初由主要研究者和同事提出，这是第一次在客观和约束值上呈现真正的非单调方面。早期的结果表明，这些属性允许优化求解器向最优点采取更少的步骤，甚至在某些情况下逃避局部最小值。

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.