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Abstract
We address the problem of training nonlinear Support Vector Machines (SVMs) with polynomial kernels, incorporating a hard cardinality constraint which fixes the number of selected features to a user-defined value B. This formulation improves interpretability by enforcing exact sparsity in the input space, but leads to a Mixed-Integer Nonlinear Program (MINLP) whose continuous relaxation is nonconvex, making it intractable for general-purpose solvers. We derive two equivalent Mixed-Integer Convex Quadratic Programming (MIQP) reformulations of the original MINLP. We prove that the continuous relaxations of the resulting formulations are convex and establish formal equivalence with the original problem. Computational experiments on benchmark datasets show that the proposed MIQP can be solved to certified global optimality in instances where the original nonconvex formulation is computationally prohibitive, confirming the practical effectiveness of the proposed approach.
Short Bio
Laura Palagi is Full Professor in Operations Research at Sapienza University of Rome, Italy. Her research has focused theoretical aspects of Mathematical Programming, mainly on continuous and mixed-integer nonlinear optimization problems, and Machine Learning and their applications. She authored around 70 papers published in international journal. She is currently the director of the PhD program in Automatic Control, Bioengineering and Operations Research at Sapienza University of Rome. She took part in the scientific committees of several international conferences. She has been member elected to the managing board of EUROPT (The Continuous Optimization Working Group of EURO) up to 2025.
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