On Fri, Aug 8, 2025 at 2:59 PM William Zijie Zhang ***@***.***> wrote: Hello all, I am starting a thread here after having an in-person discussion at ICCOPT 2025 with @TobiaMarcucci <https://github.com/TobiaMarcucci> and @AlexandreAmice <https://github.com/AlexandreAmice>. In particular, there were two major pain-points/feature requests that the gcs team talked about: 1. support for taking the perspective of a set 2. the ability to define a convex set as a list of cones (perhaps this can be a new constraint) and enforcing that a new variable belongs in this set. Some context for 1. There is already an implementation for taking the perspective of a scalar expression. see the PR <#1867>, atom <https://github.com/cvxpy/cvxpy/blob/master/cvxpy/atoms/perspective.py> and canonicalization <https://github.com/cvxpy/cvxpy/blob/master/cvxpy/reductions/dcp2cone/canonicalizers/perspective_canon.py#L25> . However taking the perspective of a set seems to require a different approach. I recall @TobiaMarcucci <https://github.com/TobiaMarcucci> mentioned that it amounts to scaling the right hand-side (b) of the conic constraint with the scalar parameter s. There was also a mention that the scalar parameter s should not be restricted to be positive, but rather another method can be used to ensure that the scaling of the perspective function is in the positive direction. (maybe I am misremembering completely though). @TobiaMarcucci <https://github.com/TobiaMarcucci>, could you provide more details of this perspective of a set formulation? (and references if possible!) I would like to read more about it to formalize things. Let me know if I said anything incorrectly above. Some context for 2. The difficulty of implementing this is that constraint objects are instantiated with the original variables as their arguments (say x), thus it is probably necessary to loop over all constraint arguments and replace any instance of x with the new variable w. @AlexandreAmice <https://github.com/AlexandreAmice> shared a code snippet which does the above. This could be a good starting point (for future reference), if we ever decide to add this feature to cvxpy. def substitute_variables_in_expression(expr, substitution_dict): if isinstance(expr, Number): return expr for key, value in substitution_dict.items(): if not isinstance(key, Leaf): raise ValueError(f"Key {key} must be of cvxpy Leaf Type") if not isinstance(value, Leaf): raise ValueError(f"Value {value} at key {key} must be of cvxpy Leaf Type") expr = expr.tree_copy() return _substitute_variables_in_expression_impl(expr, substitution_dict) def _substitute_variables_in_expression_impl(expr, substitution_dict): if isinstance(expr, Leaf): return substitution_dict.get(expr, expr) else: pass for i in range(len(expr.args)): expr.args[i] = _substitute_variables_in_expression_impl( expr.args[i], substitution_dict ) return expr I think it would be awesome to get some feedback on these two potential new features, do you have any comments and thoughts? We should also discuss about the API for these features. — Reply to this email directly, view it on GitHub <#2889>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACRLIFEX5PG4LWULI27KECD3MUMVLAVCNFSM6AAAAACDO7BL4SVHI2DSMVQWIX3LMV43ERDJONRXK43TNFXW4OZYG4YDGOBZHE> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>