In the recent literature, the connection between maximal monotone operators and the Fitzpatrick function is investigated. Subsequently, this relation has been extended to maximal monotone bifunctions and their Fitzpatrick transform. In this paper we generalize some of these results to maximal <InlineEquation ID="IEq3"> <EquationSource...</equationsource></inlineequation>

Most branch-and-bound algorithms in global optimization depend on convex underestimators to calculate lower bounds of a minimization objective function. The <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\alpha $$</EquationSource> </InlineEquation>BB methodology produces such underestimators for sufficiently smooth functions by analyzing interval Hessian approximations....</equationsource></inlineequation>

<Emphasis Type="SmallCaps">Direct-type global optimization algorithms often spend an excessive number of function evaluations on problems with many local optima exploring suboptimal local minima, thereby delaying discovery of the global minimum. In this paper, a globally-biased simplicial partition <Emphasis Type="SmallCaps">Disimpl algorithm for...</emphasis></emphasis>

We establish both necessary and sufficient optimality conditions of higher orders for various kinds of proper solutions to nonsmooth vector optimization in terms of higher-order radial sets and radial derivatives. These conditions are for global solutions and do not require continuity and...

In this paper, we extend the notions of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(\Phi ,\rho )$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Φ</mi> <mo>,</mo> <mi mathvariant="italic">ρ</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation>-invexity and generalized <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$(\Phi ,\rho )$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Φ</mi> <mo>,</mo> <mi mathvariant="italic">ρ</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation>-invexity to the continuous case and we use these concepts to establish sufficient optimality conditions for the considered class of nonconvex...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>