perf: quadratic interpolation linesearch#163
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Tests for armijo_quadratic_interp: - Full step accepted, known quadratic ϕ, overshooting backtrack - Ascent direction returns zero, safeguard clamping - Degenerate quadratic handling, x_buffer support - Solver convergence with :armijo_quadratic method - Same solution as geometric method - Warning on failure Co-Authored-By: Claude Opus 4.6 <[email protected]>
New standalone linesearch method that uses quadratic interpolation (Nocedal & Wright §3.5) after the first Armijo failure. Fits quadratic through ϕ(0), ϕ'(0)≈-2ϕ(0), ϕ(α₀) to predict the minimizer, with safeguard clamping to [0.1α, 0.5α] and division-by-zero protection. Falls back to geometric for remaining iterations if quadratic also fails. Changes: - src/linesearch.jl: Add armijo_quadratic_interp function - src/types.jl: Add :armijo_quadratic to VALID_LINESEARCH_METHODS - src/nonlinear_kkt.jl: Add :armijo_quadratic branch at linesearch call - src/MixedHierarchyGames.jl: Export armijo_quadratic_interp - test/test_nonlinear_solver_options.jl: Add :armijo_quadratic validation Co-Authored-By: Claude Opus 4.6 <[email protected]>
Compares geometric, armijo, and armijo_quadratic methods on 3-player and 4-player chain problems. Reports solve time, iterations, allocations, mean backtracks, and full-step acceptance rate. Co-Authored-By: Claude Opus 4.6 <[email protected]>
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Summary
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armijo_quadratic_interp— a new linesearch method that uses quadratic interpolation (Nocedal & Wright §3.5) to find a good step size after the first Armijo failure. Fits a quadratic through ϕ(0), ϕ'(0), and ϕ(α₀) to predict the minimizer, with safeguard clamping and fallback to geometric backtracking.Bead:
6awPR chain: PR1 (warm-start α) → PR2 (this) → PR3 (cubic interp) → PR4 (two-phase)
Changes
src/linesearch.jl: Addarmijo_quadratic_interpfunction — same interface asarmijo_backtrackingsrc/types.jl: Add:armijo_quadratictoVALID_LINESEARCH_METHODSsrc/nonlinear_kkt.jl: Add:armijo_quadraticbranch at linesearch call sitesrc/MixedHierarchyGames.jl: Exportarmijo_quadratic_interptest/test_quadratic_linesearch.jl: 12 testsets, 22 tests covering: full step, known quadratic, backtracking, ascent direction, safeguard clamping, degenerate handling, x_buffer, solver convergence, solution equivalence, warning formattest/test_tiers.jl,test/test_test_tiers.jl: Add to FAST tiertest/test_nonlinear_solver_options.jl: Add:armijo_quadraticvalidationscripts/benchmark_quadratic_linesearch.jl: Benchmark scriptTesting
julia --project=. test/test_quadratic_linesearch.jljulia --project=. scripts/benchmark_quadratic_linesearch.jlChangelog
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