Successive quadratic program,

Successive Quadratic Programming (SQP) The above approach to finding the optimum is called a feasible path method, as it attempts at all times to remain feasible with respect to the equahty and inequahty constraints as it moves to the optimum. A quite different method exists called the Successive Quadratic Programming (SQP) method, which only requires one be feasible at the final solution. Tests that compare the GRG and SQP methods generaUy favor the SQP method so it has the reputation of being one of the best methods known for nonlinear optimization for the type of problems considered here. 

Note that there are n + m equations in the n + m unknowns x and A. In Section 8.6 we describe an important class of NLP algorithms called successive quadratic programming (SQP), which solve (8.17)—(8.18) by a variant of Newton s method. 

Successive quadratic programming (SQP) methods solve a sequence of quadratic programming approximations to a nonlinear programming problem. Quadratic programs (QPs) have a quadratic objective function and linear constraints, and there exist efficient procedures for solving them see Section 8.3. As in SLP, the linear constraints are linearizations of the actual constraints about the selected point. The objective is a quadratic approximation to the Lagrangian function, and the algorithm is simply Newton s method applied to the KTC of the problem. 

Fan, Y. S. Sarkar and L. Lasdon. Experiments with Successive Quadratic Programming Algorithms. J Optim Theory Appli 56 (3), 359-383 (March 1988). 

Temet, D. J. and L. T. Biegler. Recent Improvements to a Multiplier-free Reduced Hessian Successive Quadratic Programming Algorithm. Comp Chem Engin 22 963 (1998). 

To solve the alkylation process problem, the code NPSOL, a successive quadratic programming code in MATLAB, was employed. 

Mixed-integer successive quadratic programming (refer to Chapter 9). 

Abbreviations CPU = central processing unit SQP = successive quadratic programming. 

Tjoa, I. B. and L. T. Biegler. Reduced Successive Quadratic Programming Strategy for Errors-in-Variables Estimation. Comput Chem Eng 16(6) 523-533 (1992). 

Tjoa, I. B., and Biegler, L. T. (1991). Reduced successive quadratic programming strategy for error-in-variables estimation. Comput. Chem. Eng. 16, 523-533. 

Biegler, L. T., Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation, Comp, and Chem. Eng. 8(3/4), 243-248 (1984). 

C.L. Chen, Ph.D. thesis, A class of successive quadratic programming methods for flowsheet optimization, University of London, 1988. 

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