I don't know if this is what you are looking for, but this is what comes to mind when you say Krein-Milman for cones. (I happened to be trawling the convex analysis literature for a different result... I am nowhere an expert in this.) The Krein-Milman theorem for cones that I know basically says something like (I maybe missing some details) "a closed convex cone is the convex hull of its extremal rays", and the definition of extremal ray is analogous to the definition of extremal points in convex sets: one indecomposible as a convex combination of two distinct rays.

There are more details in Convex Cones by Fuchssteiner and Lusky. Some papers that you may find useful:

• http://www.ams.org/mathscinet-getitem?mr=470662
• http://www.ams.org/mathscinet-getitem?mr=350375
• http://www.ams.org/mathscinet-getitem?mr=250012

Hope this helps.

I don't know if this is what you are looking for, but this is what comes to mind when you say Krein-Milman for cones. (I happened to be trawling the convex analysis literature for a different result... I am nowhere an expert in this.) The Krein-Milman theorem for cones that I know basically says something like (I maybe missing some details) "a closed convex cone is the convex hull of its extremal rays", and the definition of extremal ray is analogous to the definition of extremal points in convex sets: one indecomposible as a convex combination of two distinct rays.

There are more details in Convex Cones by Fuchssteiner and Lusky. Some papers that you may find useful:

• https://mathscinet.ams.org/mathscinet-getitem?mr=470662
• https://mathscinet.ams.org/mathscinet-getitem?mr=350375
• https://mathscinet.ams.org/mathscinet-getitem?mr=250012

Hope this helps.