Research map / Optimization / Nonconvex and smooth optimization
Accelerated Infeasibility Detection of Constrained Optimization and Fixed-Point Iterations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace standard fixed-point (Picard/KM) iteration with Halpern iteration (lambda_k=1/(k+1), OHM) for detecting infeasibility | PG-EXTRA on infeasible decentralized SDP · Infeasible SDP experiment | fixed-point residual convergence speed | Helped |
| Use Halpern iteration instead of Picard for normalized iterates | PG-EXTRA on infeasible decentralized SDP · Infeasible SDP experiment | normalized iterate convergence | No clear effect |
| Halpern iteration with lambda_k=1/(k+1) achieves O(1/k^2) normalized-iterate rate for infimal displacement vector | Halpern iteration on nonexpansive operators · Theory | squared normalized iterate error bound | Helped |
| Standard Picard iteration: normalized iterate rate O(1/k^2) versus O(1/k) fixed-point residual rate | Picard/KM iteration · Theory | convergence rate exponent | No clear effect |
| Matching Omega(1/k^2) lower bound established for accelerated fixed-point iterations | Fixed-point iterations satisfying linear span / deterministic · Theory | lower bound on squared error | No clear effect |
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