A review of recent advances in global optimization
Journal of Global Optimization
Branch-and-bound reduction type method for semi-infinite programming
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Nonsmooth semi-infinite programming problem using Limiting subdifferentials
Journal of Global Optimization
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This paper presents a homotopy interior point method for solving a semi-infinite programming (SIP) problem. For algorithmic purpose, based on bilevel strategy, first we illustrate appropriate necessary conditions for a solution in the framework of standard nonlinear programming (NLP), which can be solved by homotopy method. Under suitable assumptions, we can prove that the method determines a smooth interior path $$\Gamma_{w^{(0)}}\subset (X^{0}\times\mathcal{Y}^{0})\times\Re_{++}\times\Re^{l}_{++}\times(0,1]$$ from a given interior point $$w^{(0)} \in (X^{0}\times\mathcal{Y}^{0})\times\Re_{++}\times\Re^{l}_{++}$$ to a point w *, at which the necessary conditions are satisfied. Numerical tracing this path gives a globally convergent algorithm for the SIP. Lastly, several preliminary computational results illustrating the method are given.