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In this paper, a kernel-free soft quadratic surface support vector machine model is proposed for binary classification directly using a quadratic function for separation. Properties (including the solvability, uniqueness and support vector representation of the optimal solution) of the proposed model are derived. Results of computational experiments on some artificial and real-world classifying data sets indicate that the proposed soft quadratic surface support vector machine model may outperform Dagher’s quadratic model and other soft support vector machine models with a Quadratic or Gaussian kernel in terms of the classification accuracy and robustness.

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This paper develops a new model for project portfolio selection over a planning horizon with multiple time periods. The model considers the divisibility of projects and combines reinvestment, set-up cost, cardinality constraints and precedence relationship in the scheduling, simultaneously. For efficient computation, an equivalent mixed integer linear programming representation is provided. One numerical example with three scenarios is given to highlight the capability and characteristics of the proposed model.