用于基于可行路径的过程优化的改进SQP和SLSQP算法
Improved SQP and SLSQP Algorithms for Feasible Path-based Process Optimisation
AI总结：
针对病态过程优化中SQP算法的不一致子问题与数值噪声，提出改进的I-SQP和I-SLSQP算法，通过混合松弛方法和对偶LSQ抵消误差的QP求解策略，显著提升了算法的鲁棒性与计算效率。
摘要：
由于具有良好的收敛性，可行路径算法已广泛应用于过程优化。序列二次规划（SQP）算法通常用于驱动可行路径算法达到最优性。然而，现有的SQP算法可能会遇到不一致的二次规划（QP）子问题和数值噪声问题，特别是对于病态的过程优化问题，从而导致次优或不可行的解。在本研究中，我们提出了一种改进的SQP算法（I-SQP）和一种改进的序列最小二乘规划算法（I-SLSQP），该算法在每次主迭代中求解一个最小二乘（LSQ）子问题。我们提出了一种结合两种现有松弛方法的混合方法，以解决不一致的子问题，从而实现更好的收敛性和更高的效率。我们发现，对偶LSQ算法的某一部分存在严重的抵消误差，导致搜索方向不准确或无法生成可行的搜索方向。因此，在这种情况下使用QP求解器来求解LSQ子问题。计算结果表明，I-SLSQP比MATLAB中的fmincon、IPOPT、Py-SLSQP和I-SQP更鲁棒。结果还表明，对于病态的过程优化问题，I-SLSQP和Py-SLSQP优于I-SQP；而对于良态问题，I-SQP的计算效率高于I-SLSQP和Py-SLSQP。
英文摘要：
Feasible path algorithms have been widely used for process optimisation due to its good convergence. The sequential quadratic programming (SQP) algorithm is usually used to drive the feasible path algorithms towards optimality. However, existing SQP algorithms may suffer from inconsistent quadratic programming (QP) subproblems and numerical noise, especially for ill-conditioned process optimisation problems, leading to a suboptimal or infeasible solution. In this work, we propose an improved SQP algorithm (I-SQP) and an improved sequential least squares programming algorithm (I-SLSQP) that solves a least squares (LSQ) subproblem at each major iteration. A hybrid method through the combination of two existing relaxations is proposed to solve the inconsistent subproblems for better convergence and higher efficiency. We find that a certain part of the dual LSQ algorithm suffers from serious cancellation errors, resulting in an inaccurate search direction or no viable search direction generated. Therefore, the QP solver is used to solve LSQ subproblems in such a situation. The computational results indicates that I-SLSQP is more robust than fmincon in MATLAB, IPOPT, Py-SLSQP and I-SQP. It is also shown that I-SLSQP and Py-SLSQP is superior to I-SQP for ill-conditioned process optimisation problems, whilst I-SQP is more computationally efficient than I-SLSQP and Py-SLSQP for well-conditioned problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
