In deterministic continuous constrained global optimization, upper bounding the objective function generally resorts to local minimization at several nodes/iterations of the branch and bound. We propose in this paper an alternative approach when the constraints are inequalities and the feasible space has a non-null volume. First, we extract an inner region, i.e., an entirely feasible convex polyhedron or box in which all points satisfy the constraints. Second, we select a point inside the extracted inner region and update the upper bound with its cost. We describe in this paper two original inner region extraction algorithms implemented in our interval B&B called <Emphasis FontCategory="NonProportional">IbexOpt (AAAI, pp 99–104, <CitationRef CitationID="CR27">2011</CitationRef>). They apply to nonconvex constraints involving mathematical operators like , <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$ +\; \bullet ,\; /,\; power,\; sqrt,\; exp,\; log,\; sin$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo>+</mo> <mspace width="0.277778em"/> <mo>∙</mo> <mo>,</mo> <mspace width="0.277778em"/> <mo stretchy="false">/</mo> <mo>,</mo> <mspace width="0.277778em"/> <mi>p</mi> <mi>o</mi> <mi>w</mi> <mi>e</mi> <mi>r</mi> <mo>,</mo> <mspace width="0.277778em"/> <mi>s</mi> <mi>q</mi> <mi>r</mi> <mi>t</mi> <mo>,</mo> <mspace width="0.277778em"/> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mo>,</mo> <mspace width="0.277778em"/> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mo>,</mo> <mspace width="0.277778em"/> <mi>s</mi> <mi>i</mi> <mi>n</mi> </mrow> </math> </EquationSource> </InlineEquation>. This upper bounding shows very good performance obtained on medium-sized systems proposed in the <Emphasis Type="SmallCaps">COCONUT suite. Copyright Springer Science+Business Media New York 2014
