CVXPY最新版本SolverError问题排查及严格不等式疑问

Hey there, let's work through your CVXPY problems one by one!

1. SolverError After Upgrading from CVXPY 0.4 #

First off, the jump from CVXPY 0.4 to the latest version is a massive one—there were overhauls to how the library handles cone constraints and solver compatibility. Here's why you're hitting that error and how to fix it:

Why the Error Occurs #

CVXPY 0.4 was far more lenient in mapping problems to solver cones, but modern versions strictly enforce which solvers support which cone types:

• CVXOPT: Has limited support for non-linear programming cones. It struggles with ExpCone (used for log/exp-based objectives/constraints) and has restrictive SOC (second-order cone) support.
• ECOS: Supports SOC and ExpCone, but does NOT handle PSD (positive semi-definite) cones. If your problem includes PSD matrix constraints, ECOS will fail outright.

Steps to Diagnose & Fix #

• Pinpoint the problematic cone: Scan your code for:
  • SOC constraints: Things like norm(x) <= t (where t is a scalar and x is a vector)
  • ExpCone usage: Any log() or exp() terms in your objective/constraints (CVXPY converts these to exponential cone constraints)
  • PSD constraints: Variables defined with PSD=True (e.g., Variable((n,n), PSD=True)) or constraints like X >> 0
• Verify variable dimensions:
  • For PSD variables: Ensure they're square matrices (e.g., (n,n) shape, not (n,m) where n≠m)
  • For SOC constraints: Double-check that the constraint follows the standard form norm(x) <= t—modern CVXPY won't automatically reshape misaligned variables like the old 0.4 version did
• Pick the right solver:
  • If you have PSD constraints: Use SCS or MOSEK (both support all three cone types you mentioned)
  • If no PSD constraints but have SOC/ExpCone: Stick with ECOS but confirm your constraints are properly formatted
  • Avoid CVXOPT for problems involving ExpCone or complex SOC setups

2. Why CVXPY Doesn't Support Strict Inequalities #

This isn't a CVXPY limitation—it's rooted in convex optimization theory:

• In convex optimization, the feasible region for a strict inequality f(x) < b has the same closure as f(x) <= b. The optimal solution (if it exists) will lie on the boundary of the feasible region, so strict inequalities don't add practical value.
• Numerically, strict inequalities are impossible to enforce perfectly—computers can't represent infinitely small gaps.

If you need to approximate a strict inequality, use a small epsilon value:

# Instead of f(x) < b
f(x) <= b - 1e-6

Choose an epsilon that's small enough for your problem's precision requirements but not so tiny that it causes numerical instability.

内容的提问来源于stack exchange，提问作者OGARCH