We propose variants of non-asymptotic dual transcriptions for the functional inequality of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$ f + g + k\circ H \ge h$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>f</mi> <mo>+</mo> <mi>g</mi> <mo>+</mo> <mi>k</mi> <mo>∘</mo> <mi>H</mi> <mo>≥</mo> <mi>h</mi> </mrow> </math> </EquationSource> </InlineEquation>. The main tool we used consists in purely algebraic formulas on the epigraph of the Legendre-Fenchel transform of the function <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$ f + g +...</equationsource></inlineequation></equationsource></equationsource></inlineequation>

In this paper we examine non-convex quadratic optimization problems over a quadratic constraint under unknown but bounded interval perturbation of problem data in the constraint and develop criteria for characterizing robust (i.e. uncertainty-immunized) global solutions of classes of non-convex...

In this paper we present necessary conditions for global optimality for polynomial problems with box or bivalent constraints using separable polynomial relaxations. We achieve this by first deriving a numerically checkable characterization of global optimality for separable polynomial problems...