基于最小自由能法的理想气相反应平衡新算法

针对目前采用最小自由能法计算理想气相反应平衡问题存在的不足，提出了梯度投影拉格朗日算法。算法中，采用了弱收敛准则作为梯度投影法的收敛标准，并从数学上证明了梯度投影法采用弱收敛条件的合理性和算法的收敛性，基于此，将梯度投影法的计算结果作为牛顿法计算拉格朗日乘数法的计算初值，同时对牛顿法的迭代步长进行了改进，从而解决了牛顿法计算初值选取困难的问题，提高了算法的稳健性和计算速度。算例计算结果表明，该算法的收敛速度快且计算精度高。

Novel Algorithm for Calculating Ideal Gas Phase Reactions Based on the Minimization of Free Energy

In this work, we propose a gradient projected Lagrangian algorithm to address the inadequacies of current free-energy minimization-based solution method for calculating the composition of the ideal gas phase equilibrium. In this algorithm, a weak convergence criterion was used as the convergence criterion of the gradient projection method. Mathematical proofs were then provided for the rationality of the weak convergence conditions used in the gradient projection method, as well as the convergence of this algorithm. On this basis, the result calculated by the gradient projection method was used as the initial value in Newton's method with Lagrange multipliers, and improvements were also made on the iteration step used in Newton's method. We have thus resolved the difficulty of selecting an initial value for Newton's method, and improved the stability and computational speed of the algorithm. The results of example calculations demonstrated that the algorithm proposed in this work converges very quickly and exhibits a high level of computational accuracy.