48 A Hybrid Method for Global Optimization of Multivariate Polynomial
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A hybrid algorithm for global optimization of multivariate polynomial with bound constraints was proposed. The algorithm combines numerical, interval and symbolic methods. Interval methods can obtain small intervals and are guaranteed to contain the global optimum in the presence of rounding errors. Almost all interval-based global optimization methods use interval Newton method to verify existence and uniqueness of a solution to the problem. However, existence and uniqueness verification of a solution to a problem will not succeed when the Jacobi matrix is singular at some point in the region. To overcome the interval methods' shortcomings, we propose to use the symbolic method proposed by Pedersen et al. to improve the system's efficiency and to guarantee the interval methods' integrity. The hybrid method can solve problems that separately none of traditional methods is unable to solve. Furthermore, all the methods in our algorithm have nice properties for parallelization. So the performance of the system can be improved further.