# t8 - Basic Procedure An integer linear program is a linear...

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Basic Procedure An integer linear program is a linear program further constrained by the integrality restrictions. Thus, in a maximization problem, the value of the objective function, at the linear-program optimum, will always be an upper bound on the optimal integer-programming objective. In addition, any integer feasible point is The use of Mercer's theorem for interpreting kernels as inner products in a feature space was introduced into machine learning in 1964 by the work of Aizermann, Bravermann and Rozoener on the method of potential functions [1], but its possibilities were not fully understood until it was first used in the article by Boser, Guyon and Vapnik that introduced the Support Vector method [19]. The theory of kernels is, however, older: Mercer's theorem dates back to 1909 [95], and the study of reproducing kernel Hilbert spaces was developed by Aronszajn in the 1940s [7]. This theory was used in approximation and regularisation theory, see for example the book of Wahba [171] and her 1999 survey [172]. The first use of polynomial kernels was by Poggio in 1975 [115]. Reproducing kernels were extensively used in machine learning and neural networks by Poggio and Girosi, see for example their 1990 paper on radial basis function networks [116]. The theory of positive definite functions was also developed in the context of covariance and correlation functions, so

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t8 - Basic Procedure An integer linear program is a linear...

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