Annals of Operations Research
A new computational algorithm for functional inequality constrained optimization problems
Automatica (Journal of IFAC)
Optimization by Vector Space Methods
Optimization by Vector Space Methods
A New Quadratic Semi-infinite Programming Algorithm Based on Dual Parametrization
Journal of Global Optimization
A relaxed cutting plane method for semi-infinite semi-definite programming
Journal of Computational and Applied Mathematics
Numerical method for a class of optimal control problems subject to nonsmooth functional constraints
Journal of Computational and Applied Mathematics
A review of recent advances in global optimization
Journal of Global Optimization
A dual parametrization approach to Nyquist filter design
Signal Processing
A New Exchange Method for Convex Semi-Infinite Programming
SIAM Journal on Optimization
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The so called dual parametrization method for quadratic semi-infinite programming (SIP) problems is developed recently for quadratic SIP problems with a single infinite constraint. A dual parametrization algorithm is also proposed for numerical solution of such problems. In this paper, we consider quadratic SIP problems with positive definite objective and multiple linear infinite constraints. All the infinite constraints are supposed to be continuously dependent on their index variable on a compact set which is defined by a number equality and inequalities. We prove that in the multiple infinite constraint case, the minimu parametrization number, just as in the single infinite constraint case, is less or equal to the dimension of the SIP problem. Furthermore, we propose an adaptive dual parametrization algorithm with convergence result. Compared with the previous dual parametrization algorithm, the adaptive algorithm solves subproblems with much smaller number of constraints. The efficiency of the new algorithm is shown by solving a number of numerical examples.