"Reduced Hessian SQP: KWIK算法1应用研究"

Quadratic Programming Methods for Reduced Hessian SQP is a research paper published in Computers and Chemical Engineering Vol. 18, No. 9 in 1994. The authors, C. Schmid and L. T. Biegler, from the Chemical Engineering Department at Carnegie Mellon University in Pittsburgh, present a new algorithm known as KWIK algorithm 1 for solving quadratic programming problems in the context of Sequential Quadratic Programming (SQP). The paper discusses the importance of solving quadratic programming problems efficiently, especially in the field of chemical engineering where optimization plays a crucial role. The authors highlight the limitations of traditional SQP algorithms that rely on the full Hessian matrix, which can be computationally expensive for large-scale optimization problems. To address this issue, Schmid and Biegler propose a novel approach that utilizes a reduced Hessian matrix to accelerate the convergence of the optimization process. The Reduced Hessian SQP algorithm aims to improve the efficiency of solving quadratic programming problems by exploiting the structure of the reduced Hessian matrix. By considering only the most significant elements of the Hessian matrix, the algorithm reduces the computational burden while still maintaining the accuracy of the solution. The authors provide detailed theoretical analysis and numerical results to demonstrate the effectiveness of their approach in various optimization scenarios. Overall, the paper contributes to the field of optimization by introducing a new algorithm that offers a more efficient solution to quadratic programming problems. The Reduced Hessian SQP algorithm has the potential to significantly improve the performance of optimization algorithms in various engineering and scientific applications. The research presented in this paper opens up new possibilities for developing advanced optimization techniques that can address complex real-world problems more effectively.