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Brainstorming Disable-able Constraints for CVXPY

I've analyzed the CVXPY codebase to understand how constraints and DPP work. Here are several approaches for implementing disable-able constraints while maintaining full DPP compatibility.

Background: Key DPP Requirements

For context, DPP (Disciplined Parametrized Programming) allows fast re-solving by:

Treating Parameters as affine expressions (not constants) during curvature analysis
Caching the problem's canonicalized form so parameter values can be substituted without re-compilation
Requiring that all expressions remain properly disciplined when parameters are treated as affine

Any disable-able constraint feature must preserve these properties.

Approach 1: Boolean Parameter with Indicator Constraints

Concept: Use a boolean/binary Parameter to control whether a constraint is enforced, leveraging CVXPY's existing indicator functionality.

Implementation:

# User code
x = cp.Variable()
enabled = cp.Parameter(value=1)  # 1 = enabled, 0 = disabled

# Option 1a: Using indicator constraints (if available)
constraint = cp.constraints.Indicator(enabled == 1, x >= 0)

# Option 1b: Using large slack approach
M = 1e6  # Big-M constant
constraint = x >= -M * (1 - enabled)  # When enabled=1: x >= 0; when enabled=0: x >= -M

DPP Analysis:

✅ DPP Compatible: Parameters remain affine in the constraint expression
✅ Fast re-solving: Changing enabled.value doesn't require recompilation
✅ No API changes: Works with existing CVXPY infrastructure

Pros:

Already implementable with existing CVXPY features
No changes to core constraint classes needed
Mathematically clean: constraint is either enforced or made trivially satisfiable
DPP-compatible by construction

Cons:

Big-M approach requires choosing appropriate M (problem-dependent)
Big-M can cause numerical issues for some solvers
Verbose syntax for users
Doesn't truly "disable" constraint (just makes it always satisfied)
Indicator constraints may not be supported by all solvers

DPP Compatibility: ⭐⭐⭐⭐⭐ Fully compatible

Approach 2: Constraint Wrapper with Parameter-Based Filtering

Concept: Add a lightweight wrapper or attribute to constraints that uses a Parameter to indicate if the constraint should be included during compilation.

Implementation:

# New API methods on Constraint class
class Constraint:
    def __init__(self, args, constr_id=None, enabled=None):
        # ... existing code ...
        self._enabled_param = enabled  # Parameter or None
    
    def is_enabled(self):
        """Check if constraint is currently enabled"""
        if self._enabled_param is None:
            return True
        if self._enabled_param.value is None:
            raise ValueError("Enabled parameter must have a value")
        return bool(self._enabled_param.value)
    
    def set_enabled(self, enabled_param):
        """Set parameter controlling whether constraint is enabled"""
        if not isinstance(enabled_param, Parameter):
            raise TypeError("enabled must be a Parameter")
        self._enabled_param = enabled_param
        return self

# User code
x = cp.Variable()
enabled = cp.Parameter(value=True)
constraint = (x >= 0).set_enabled(enabled)

# Problem compilation filters constraints
constraints = [c for c in problem.constraints if c.is_enabled()]

DPP Analysis:

❌ NOT DPP Compatible: Filtering constraints based on parameter values happens at compile time
❌ No fast re-solving: Changing enabled.value requires full recompilation since constraint set changes
⚠️ Breaks DPP caching: The canonicalized problem structure changes when constraints are added/removed

Pros:

Clean, intuitive API
Truly disables constraints (not in problem at all)
No numerical issues like Big-M
Easy to implement

Cons:

Breaks DPP: Constraint set changes require recompilation, losing DPP benefits
Cache invalidation complexity
Constraint IDs and dual variables become inconsistent across solves

DPP Compatibility: ⭐ Not compatible

Approach 3: Parameter-Affine Constraint Relaxation

Concept: Instead of removing constraints, parameterize them to smoothly relax toward "always satisfied" state using parameter values. Keep constraint in problem but make it trivially satisfiable.

Implementation:

# Add method to Constraint base class
class Constraint:
    def relaxed(self, slack_param):
        """Return a relaxed version of this constraint
        
        Creates a new constraint with parameter-controlled slack.
        When slack_param = 0, constraint is fully enforced.
        When slack_param → ∞, constraint becomes trivially satisfied.
        """
        # For x >= 0, becomes x + slack_param >= 0
        # For x <= b, becomes x <= b + slack_param
        # For x == 0, becomes x == slack_param (or ||x|| <= slack_param)
        pass

# User code
x = cp.Variable()
slack = cp.Parameter(value=0, nonneg=True)  # 0 = enabled, large = disabled
constraint = (x >= 5).relaxed(slack)

# To disable: slack.value = 1e6
# To enable: slack.value = 0

DPP Analysis:

✅ DPP Compatible: Slack parameter is affine in constraint expression
✅ Fast re-solving: Constraint structure unchanged, only parameter values change
✅ Same problem structure: All constraints always present

Pros:

Maintains DPP compatibility perfectly
Smooth relaxation allows "partial" enabling (useful for homotopy methods)
Constraint and dual variable structure stays consistent
No Big-M numerical issues if properly bounded
Clean API

Cons:

Need to choose appropriate slack values (problem-dependent)
Relaxed constraints still consume solver resources
Dual variables of "disabled" constraints may not be meaningful
Equality constraints require special handling (can't use simple slack)
Implementation complexity: each constraint type needs custom relaxation logic

DPP Compatibility: ⭐⭐⭐⭐⭐ Fully compatible

Approach 4: Multi-Parameter with Conditional Compilation

Concept: Create a special problem compilation mode that treats different parameter values as different "scenarios", each with its own constraint set, but share variable structure.

Implementation:

# Problem tracks constraint scenarios
class Problem:
    def add_conditional_constraint(self, constraint, enabled_param):
        """Add constraint that's only active when enabled_param == 1"""
        self._conditional_constraints[enabled_param].append(constraint)
    
    def solve(self, **kwargs):
        # Build active constraint set based on current parameter values
        active_constraints = self._always_constraints.copy()
        for param, constraints in self._conditional_constraints.items():
            if param.value == 1:
                active_constraints.extend(constraints)
        # Solve with active constraints
        pass

# User code
x = cp.Variable()
enabled = cp.Parameter(value=1)
prob = cp.Problem(cp.Minimize(x**2))
prob.add_conditional_constraint(x >= 0, enabled)

DPP Analysis:

❌ NOT DPP Compatible: Problem structure changes based on parameter values
❌ Defeats DPP purpose: Requires recompilation when enabled parameters change
⚠️ Complex caching: Would need to cache multiple problem variants

Pros:

Truly disables constraints
Could potentially cache multiple "scenarios"
Flexible API

Cons:

Incompatible with DPP philosophy: Constraint set shouldn't depend on parameter values
Complex implementation and caching logic
Multiple cached problem variants consume memory
Doesn't scale to many conditional constraints

DPP Compatibility: ⭐ Not compatible

Approach 5: Hybrid - Slack Parameter with Smart Defaults

Concept: Extend Approach 3 with automatic bound computation and helper methods for common cases.

Implementation:

# Enhanced Constraint class
class Constraint:
    def with_enable_parameter(self, enabled_param, auto_bounds=True):
        """Add an enable/disable parameter to this constraint
        
        Parameters:
            enabled_param: Parameter (value 0 = disabled, 1 = enabled)
            auto_bounds: If True, automatically compute problem bounds
        
        Returns:
            Modified constraint with slack term
        """
        if auto_bounds:
            slack = cp.Parameter() * (1 - enabled_param)
            slack._auto_bound = True  # Signal to Problem to compute bounds
        else:
            slack = cp.Parameter() * (1 - enabled_param)
        
        # Return relaxed constraint
        return self._add_slack(slack)

# User code - simple case
x = cp.Variable()
enabled = cp.Parameter(value=1)
constraint = (x >= 0).with_enable_parameter(enabled, auto_bounds=True)

prob = cp.Problem(cp.Minimize(x), [constraint])
prob.solve()  # Auto-computes appropriate slack bounds

enabled.value = 0  # Disable constraint
prob.solve()  # Fast re-solve with DPP

enabled.value = 1  # Re-enable constraint
prob.solve()  # Fast re-solve with DPP

DPP Analysis:

✅ DPP Compatible: Uses parameter-affine slack approach
✅ Fast re-solving: Structure unchanged, only parameters change
✅ Automatic handling: Reduces user burden of choosing bounds

Pros:

Maintains full DPP compatibility
More user-friendly than manual slack selection
Could analyze problem to compute safe bounds automatically
Clear semantic: enabled=1 means enforced, enabled=0 means disabled
Could provide warnings if bounds seem insufficient

Cons:

Auto-bound computation is heuristic (may be conservative or insufficient)
Still has some numerical considerations
Implementation complexity in bound analysis
Disabled constraints still in solver (small performance cost)

DPP Compatibility: ⭐⭐⭐⭐⭐ Fully compatible

Approach 6: Epigraph Reformulation with Parameter

Concept: For inequality constraints, reformulate using an auxiliary variable and parameter-controlled bound.

Implementation:

# For constraint f(x) <= 0, reformulate as:
#   t >= 0
#   f(x) <= t
#   t <= M * (1 - enabled)
# When enabled=1: t <= 0, so f(x) <= 0 (enforced)
# When enabled=0: t <= M (relaxed)

class Constraint:
    def epigraph_disabled(self, enabled_param, M=1e6):
        """Create epigraph form with enable parameter"""
        # Returns: list of constraints with auxiliary variable
        pass

# User code
x = cp.Variable()
enabled = cp.Parameter(value=1)
constraints = (x >= 0).epigraph_disabled(enabled)  # Returns list

DPP Analysis:

✅ DPP Compatible: All constraints use parameters in affine way
✅ Fast re-solving: Structure fixed, parameters vary
⚠️ More variables: Introduces auxiliary variables

Pros:

DPP compatible
Mathematically clean separation of concerns
Works well for inequality constraints
Auxiliary variables may be beneficial for some solvers

Cons:

Increases problem size (more variables and constraints)
Still has Big-M issues
Not applicable to all constraint types
More complex for users to understand

DPP Compatibility: ⭐⭐⭐⭐ Mostly compatible (with Big-M caveats)

Recommended Approach: Hybrid (Approach 5)

I recommend Approach 5 for the following reasons:

Full DPP Compatibility: Uses parameter-affine slack approach that maintains DPP's fast re-solving benefits
User-Friendly: API like constraint.with_enable_parameter(enabled) is intuitive
Handles Common Cases Well: Auto-bound computation helps users avoid choosing arbitrary Big-M values
Incrementally Implementable: Start simple (manual slack bounds), add auto-bounds later
Maintains Consistency: Constraint and dual variable structure never changes

Suggested Implementation Plan:

Phase 1: Basic functionality

class Constraint:
    def with_slack_parameter(self, slack_param):
        """Add parameter-controlled slack to constraint"""
        # Implement for each constraint type
        pass

Phase 2: Enable/disable convenience

class Constraint:
    def with_enable_parameter(self, enabled_param, slack_value=1e6):
        """Add enable/disable parameter (user provides slack value)"""
        slack = slack_value * (1 - enabled_param)
        return self.with_slack_parameter(slack)

Phase 3: Smart defaults

class Constraint:
    def with_enable_parameter(self, enabled_param, auto_bounds=True):
        """Add enable/disable with automatic bound computation"""
        if auto_bounds:
            # Analyze problem to compute safe slack bounds
            slack = self._compute_auto_slack(enabled_param)
        else:
            slack = 1e6 * (1 - enabled_param)
        return self.with_slack_parameter(slack)

Alternative: Approach 3 (Simpler)

If automatic bound computation is too complex, Approach 3 (manual relaxation) is a solid fallback:

# Simpler API, user responsible for bounds
constraint = (x >= 0).relaxed(slack_param)

This is still DPP-compatible and gives users full control, at the cost of requiring them to understand their problem's scale.

What NOT to Do

Avoid Approaches 2 and 4 that filter constraints based on parameter values. These fundamentally break DPP because:

The problem structure changes when constraints are added/removed
Cached compilation becomes invalid
You lose the fast re-solving benefit that DPP provides

The key insight: DPP requires the problem structure to remain constant. Parameters should control values, not structure.

Summary

The core challenge is balancing user convenience with DPP's requirement that problem structure remain constant. The best approaches use parameter-affine slack/relaxation terms to keep constraints in the problem while making them trivially satisfiable when "disabled". This maintains DPP's fast re-solving while providing the disable-able constraint functionality users need.

Disable-able Constraints #3041

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