Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Quadratic Eigenvalue Complementarity Problem (QEiCP) is an extension of the Eigenvalue Complementarity Problem (EiCP) that has been introduced recently. Similar to the EiCP, the QEiCP always has a solution under reasonable hypotheses on the matrices included in its definition. This has been established in a previous paper by reducing a QEiCP of dimension n to a special 2n-order EiCP.   propose an enumerative algorithm for solving the QEiCP by exploiting this equivalence with an EiCP. The algorithm seeks a global minimum of a special Nonlinear Programming Problem (NLP) with a known global optimal value. The algorithm is shown to perform very ll in practice but in some cases terminates with only an approximate optimal solution to NLP. Hence,  propose a hybrid method that combines the enumerative method with a fast and local semi-smooth method to overcome the latter drawback. This algorithm is also shown to be useful for computing a positive eigenvalue for an EiCP under similar assumptions. Computational experience is reported to demonstrate the efficacy and efficiency of the hybrid enumerative method for solving the QEiCP.
['Alfredo N. Iusem', 'Joaquim J. Júdice', 'Valentina Sessa', 'Hanif D. Sherali']
I am writing a research paper on a idea On the numerical solution of the quadratic eigenvalue complementarity problem
[{"from": "human", "value": "I am writing a research paper on a idea On the numerical solution of the quadratic eigenvalue complementarity problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Quadratic Eigenvalue Complementarity Problem (QEiCP) is an extension of the Eigenvalue Complementarity Problem (EiCP) that has been introduced recently. Similar to the EiCP, the QEiCP always has a solution under reasonable hypotheses on the matrices included in its definition. This has been established in a previous paper by reducing a QEiCP of dimension n to a special 2n-order EiCP.   propose an enumerative algorithm for solving the QEiCP by exploiting this equivalence with an EiCP. The algorithm seeks a global minimum of a special Nonlinear Programming Problem (NLP) with a known global optimal value. The algorithm is shown to perform very ll in practice but in some cases terminates with only an approximate optimal solution to NLP. Hence,  propose a hybrid method that combines the enumerative method with a fast and local semi-smooth method to overcome the latter drawback. This algorithm is also shown to be useful for computing a positive eigenvalue for an EiCP under similar assumptions. Computational experience is reported to demonstrate the efficacy and efficiency of the hybrid enumerative method for solving the QEiCP."}]