Semi-infinite quadratic optimization method using dual parametrization with application to antenna array

Abstract

In this article, we consider the practical application of the dual parametrization method for semi-infinite quadratic optimization problems. It is known that the efficiency of the dual parametrization algorithm depends on the method used in its final local search step. For some practical problems, the variables representing the index points in the parametrized dual problem may be sensitive and available local search methods may have difficulty finding the precise optimal locations of the index positions. Thus, we propose modifications to the dual parametrization algorithm developed earlier to overcome these problems. The modified algorithm is applied to a general design of antenna arrays. Numerical results are compared with other design methods.

¶Dedicated to N.U. Ahmed on the occassion of his 70th birthday.

Keywords:

• Semi-infinite optimization
• Quadratic optimization
• Dual parametrization algorithm

Keywords:

• Mathematics Subject Classifications 2000:
• 90C34
• 90C20
• 65K05

Acknowledgment

The work was partly sponsored by ARC under grant no. DP0451111.

Notes

¶Dedicated to N.U. Ahmed on the occassion of his 70th birthday.