Sparse optimization and SDP-based post-processing of PEP dual certificates recovers compact, interpretable proofs and Lyapunov functions for first-order optimization methods.
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Framework converts tight analytic convergence proofs into Lyapunov-style ones via PEP and linear algebra, reproduces prior analyses, and yields four new proofs including a novel optimal proximal algorithm for strongly monotone inclusions.
Chambolle-Pock converges weakly to a KKT point for 0 < θ ≤ 1 when τσ‖L‖² is below 4θ(2-θ)/(1-2θ+9θ²-4θ³), with ergodic duality gap O(1/k).
citing papers explorer
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Finding Simple Proofs for First-Order Optimization
Sparse optimization and SDP-based post-processing of PEP dual certificates recovers compact, interpretable proofs and Lyapunov functions for first-order optimization methods.
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Toward a Systematic Understanding and Interactive Search of Lyapunov-Style Proofs in Optimization
Framework converts tight analytic convergence proofs into Lyapunov-style ones via PEP and linear algebra, reproduces prior analyses, and yields four new proofs including a novel optimal proximal algorithm for strongly monotone inclusions.
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The Chambolle-Pock method also converges weakly with $0 < \theta \le 1$ and $\tau\sigma\|L\|^{2} < 4\theta(2-\theta)/(1 - 2\theta + 9\theta^{2} - 4\theta^{3})$
Chambolle-Pock converges weakly to a KKT point for 0 < θ ≤ 1 when τσ‖L‖² is below 4θ(2-θ)/(1-2θ+9θ²-4θ³), with ergodic duality gap O(1/k).