We investigate in this paper the duality gap between quadratic knapsack problem and its Lagrangian dual or semidefinite programming relaxation. We characterize the duality gap by a distance measure from set {0, 1}<Superscript> n </Superscript> to certain polyhedral set and demonstrate that the duality gap can be reduced...</superscript>

Computing a sample mean of time series under dynamic time warping is NP-hard. Consequently, there is an ongoing research effort to devise efficient heuristics. The majority of heuristics have been developed for the constrained sample mean problem that assumes a solution of predefined length. In...

Current generalizations of the central ideas of single-objective branch-and-bound to the multiobjective setting do not seem to follow their train of thought all the way. The present paper complements the various suggestions for generalizations of partial lower bounds and of overall upper bounds...

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...

We propose and study a new method, called the Interior Epigraph Directions (IED) method, for solving constrained nonsmooth and nonconvex optimization. The IED method considers the dual problem induced by a generalized augmented Lagrangian duality scheme, and obtains the primal solution by...

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...

In this work, by using weak conjugate maps given in (Azimov and Gasimov, in Int J Appl Math 1:171–192, <CitationRef CitationID="CR1">1999</CitationRef>), weak Fenchel conjugate dual problem, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${(D_F^w)}$$</EquationSource> </InlineEquation> , and weak Fenchel Lagrange conjugate dual problem <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${(D_{FL}^w)}$$</EquationSource> </InlineEquation> are constructed. Necessary and sufficient conditions for...</equationsource></inlineequation></equationsource></inlineequation></citationref>