This paper presents the surrogate model based algorithm SO-I for solving purely integer optimization problems that have computationally expensive black-box objective functions and that may have computationally expensive constraints. The algorithm was developed for solving global optimization...

Multivariate adaptive regression splines (MARS) has become a popular data mining (DM) tool due to its flexible model building strategy for high dimensional data. Compared to well-known others, it performs better in many areas such as finance, informatics, technology and science. Many studies...

This paper considers the optimization problem of minimizing a rational function. We reformulate this problem as a polynomial optimization problem by the technique of homogenization. These two problems are shown to be equivalent under some generic conditions. The exact Jacobian SDP relaxation...

Stochastic optimization methods such as evolutionary algorithms and Markov Chain Monte Carlo methods usually involve a Markov search of the optimization domain. Evolutionary annealing is an evolutionary algorithm that leverages all the information gathered by previous queries to the cost...

In this paper we present necessary conditions for global optimality for polynomial problems with box or bivalent constraints using separable polynomial relaxations. We achieve this by first deriving a numerically checkable characterization of global optimality for separable polynomial problems...

Three rejection tests for multi-objective optimization problems based on first order optimality conditions are proposed. These tests can certify that a box does not contain any local minimizer, and thus it can be excluded from the search process. They generalize previously proposed rejection...

Trust region algorithms are well known in the field of local continuous optimization. They proceed by maintaining a confidence region in which a simple, most often quadratic, model is substituted to the criterion to be minimized. The minimum of the model in the trust region becomes the next...