Quadratic programming solver for large-scale structural optimization using SQP algorithm

The primal/dual quadratic programming algorithm of Goldfarb and Idnani is implemented as a solver for a Sequential Quadratic Programming algorithm. Initially the algorithm is briefly described. As the algorithm requires the inverse of the Cholesky factor of the Hessian matrix at each iteration a procedure is presented to directly obtain a matrix that multiplied by its transpose gives the BFGS update of the Hessian. A procedure is then presented to triangularise the updated factor using two series of Givens rotations. In order to increase efficiency a "warm start" strategy is proposed whereby the choice of constraints to enter the active set is based on information of previous SQP iterations. Finally two examples are given to demonstrate the efficiency and robustness of the implementation.