The inverse max + sum spanning tree (IMSST) problem is studied, which is the first inverse problem on optimization problems with combined minmax–minsum objective functions. Given an edge-weighted undirected network <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$G(V,E,c,w)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>G</mi> <mo stretchy="false">(</mo> <mi>V</mi> <mo>,</mo> <mi>E</mi> <mo>,</mo> <mi>c</mi> <mo>,</mo> <mi>w</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation>, the MSST problem is to find a...</equationsource></equationsource></inlineequation>