Application of Sequential Quadratic Programming Based on Active Set Method in Cleaner Production

On the platform of general chemical process simulation software(it was named Optimization Engineer, OPEN), a general optimization algorithm for chemical process simulation is developed using C++ code. The algorithm is based on Sequential Quadratic Programming (SQP). We adopt the activity set algorithm and the rotation axis algorithm to generate the activity set to solve the quadratic programming sub-problem. The active set method can simplify the number of constraints and speed up the calculation. At the same time, we used limited memory BFGS algorithm (L-BFGS) to simplify the solution of second derivative matrix. The special matrix storage mode of L-BFGS algorithm can save the storage space and speed up the computing efficiency. We use exact penalty function and traditional step-size rule in the algorithm. These two methods can ensure the convergence of the algorithm, a more correct search direction and suitable search step. The example shows that the advanced optimization function can meet the requirements of General Chemical Process Calculation. The number of iterations can reduce by about 6.0% . The computation time can reduce by about 6.5% . We combined this algorithm with chemical simulation technology to develop the optimization function of chemical engineering simulation. This optimization function can play an important role in the process optimization calculation aiming at energy saving and green production.

Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models

In this work, a new heuristic computing design is presented with an artificial intelligence approach to exploit the models with feed-forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of genetic algorithms (GA) combined with local convergence aptitude of active-set method (ASM), i.e., FF-GNN-GAASM to solve the second kind of Lane–Emden nonlinear singular models (LE-NSM). The proposed method based on the computing intelligent Gudermannian kernel is incorporated with the hidden layer configuration of FF-GNN models of differential operatives of the LE-NSM, which are arbitrarily associated with presenting an error-based objective function that is used to optimize by the hybrid heuristics of GAASM. Three LE-NSM-based examples are numerically solved to authenticate the effectiveness, accurateness, and efficiency of the suggested FF-GNN-GAASM. The reliability of the scheme via statistical valuations is verified in order to authenticate the stability, accuracy, and convergence.

Primal-dual active-set method for solving the unilateral pricing problem of American better-of options on two assets

<abstract><p>In this paper, an efficient numerical algorithm is proposed for the valuation of unilateral American better-of options with two underlying assets. The pricing model can be described as a backward parabolic variational inequality with variable coefficients on a two-dimensional unbounded domain. It can be transformed into a one-dimensional bounded free boundary problem by some conventional transformations and the far-field truncation technique. With appropriate boundary conditions on the free boundary, a bounded linear complementary problem corresponding to the option pricing is established. Furthermore, the full discretization scheme is obtained by applying the backward Euler method and the finite element method in temporal and spatial directions, respectively. Based on the symmetric positive definite property of the discretized matrix, the value of the option and the free boundary are obtained simultaneously by the primal-dual active-set method. The error estimation is established by the variational theory. Numerical experiments are carried out to verify the efficiency of our method at the end.</p></abstract>