Ttdfjt

I am using the following code:

documentclassarticle
usepackagecases
usepackageamsmath,amsfonts
begindocument

beginalign*
 undersettau in mathbbRmin tau
endalign*
beginsubnumcasestextrms.t. forall w in dom f^*, exists lambda in mathbbR^q: 
 d^top lambda + w^top b - f^*(w) leq 0 \
 D^top lambda geq A^top w \
 lambda geq mathbf0
endsubnumcases

enddocument

To produce the following:

I am happy with the result, but I don't feel like I am doing the correct thing. Both of the min term and s.t. term belong to the same optimization problem. When I define the minimization line with align* and the constraints with subnumcases, then there are problems like:

1. A new page can start right after the 'min' part


2. When I use label, ref, then it says Problem (3.2), but actually, the min tau line is not in Problem 3.2


3. In similar but bigger problems, the alignment looks odd

Thus, I will be very happy to hear some suggestions!

I'd probably just use cases but if you definitely want the subnumcases layout you could use a minipage to keep things together.

documentclassarticle
usepackagemathtools,amsfonts,cases
DeclareMathOperatordomdom
begindocument

using gather
begingather*
 min_tau in mathbbR tau\
shortintertexts.t.
forall w in dom f^*, exists lambda in mathbbR^q
begincases
 d^top lambda + w^top b - f^*(w) leq 0 \
 D^top lambda geq A^top w \
 lambda geq mathbf0
endcases
endgather*


a\a\a\a\a\a\a\a\
a\a\a\a\a\a\a\a\
a\a\a\a\a\a\a\a\
a\a\a\a\a\a\a\a\
a\a\a

using [\
noindentbeginminipagetextwidth
noindent[
 min_tau in mathbbR tau\
]
s.t.
beginsubnumcases
forall w in dom f^*, exists lambda in mathbbR^q
 d^top lambda + w^top b - f^*(w) leq 0 \
 D^top lambda geq A^top w \
 lambda geq mathbf0
endsubnumcases
endminipage
enddocument

I propose this variant layout, using the facilities of the optidef package, dedicated to the layout of optimisation problems:

documentclassarticle
usepackagemathtools, amsfonts
usepackage[short]optidef
usepackagecleveref 
DeclareMathOperatordomdom

begindocument

 beginmini!
 mathclaptauinmathbbRtau notag
 
 addConstraint d^top lambda + w^top b - f^*(w) leq 0labeleqa
 addConstraintforall w in dom f^*, exists lambda in mathbbR^q:smashbegincases\\\endcaseshspace*-1emD^top lambda geq A^top w labeleqb
 addConstraintlambda geq mathbf0labeleqc
 endmini!
We can see from crefeqa,eqb,eqc

enddocument