• 대한수학회지
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• 제56권4호
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• pp.1001-1016
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• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1999년도 추계종합학술대회 논문집
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• pp.732-735
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• 1999

A GA-based optimization technique is adopted in the paper to obtain optimal future control inputs for predictive control systems. For reliable future predictions of a process, we identify the underlying process with an NNARX model structure and investigate to reduce the volume of neural network based on the Lipschitz index and a criterion. Since most industrial processes are subject to their constraints, we deal with the input-output constraints by modifying some genetic operators and/or using a penalty strategy in the GAPC. Some computer simulations are given to show the effectiveness of the GAPC method compared with the adaptive GPC algorithm.