A deterministic global optimization method is developed for a class of discontinuous functions. McCormick’s method to obtain relaxations of nonconvex functions is extended to discontinuous factorable functions by representing a discontinuity with a step function. The properties of the...

This article presents an analysis of the convergence order of Taylor models and McCormick-Taylor models, namely Taylor models with McCormick relaxations as the remainder bounder, for factorable functions. Building upon the analysis of McCormick relaxations by Bompadre and Mitsos (J Glob Optim...

We propose in this paper a fixed parameter polynomial algorithm for the cardinality-constrained quadratic optimization problem, which is NP-hard in general. More specifically, we prove that, given a problem of size n (the number of decision variables) and s (the cardinality), if the n−k...

This paper investigate a class of semi-supervised support vector machines (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\text{ S }^3\mathrm{VMs}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mspace width="4.pt"/> <mtext>S</mtext> <msup> <mspace width="4.pt"/> <mn>3</mn> </msup> <mi mathvariant="normal">VMs</mi> </mrow> </math> </EquationSource> </InlineEquation>) with arbitrary norm. A general framework for the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\text{ S }^3\mathrm{VMs}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mspace width="4.pt"/> <mtext>S</mtext> <msup> <mspace width="4.pt"/> <mn>3</mn> </msup> <mi mathvariant="normal">VMs</mi> </mrow> </math> </EquationSource> </InlineEquation> was first constructed based on a robust DC (Difference of Convex...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

We present a new way to solve generalized Nash equilibrium problems. We assume the feasible set to be compact. Furthermore all functions are assumed to be polynomials. However we do not impose convexity on either the utility functions or the action sets. The key idea is to use Putinar’s...