cvxpy port

FORMULATION_AUDIT.md

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+# RKHS Formulation Audit
+
+This repository uses ridgeless RKHS collocation: each independent kernel
+function is identified by including its squared RKHS norm, `alpha' K alpha`,
+in the objective. The active implementation uses direct JAX callbacks into UNO.
+
+## Asset Pricing
+
+- RKHS functions: asset price/costate `p`.
+- Algebraic helpers: none.
+- Objective: `||p||_H^2`.
+- Constraints: collocated asset-pricing ODE `dp/dt = r p - x(t)`.
+- Solver implementation: direct JAX/UNO quadratic model.
+
+## Basic Neoclassical Growth
+
+- RKHS functions: capital `k`, consumption `c`, costate `mu`.
+- Algebraic helpers: none.
+- Objective: `||k||_H^2 + ||c||_H^2 + ||mu||_H^2`.
+- Constraints: resource equation, Euler equation, `mu*c = 1`, and positive
+  domain guards for `k`, `c`, and `mu`.
+- Solver implementation: direct JAX/UNO nonlinear model; adding the `c` norm
+  removes the former under-identification of consumption coefficients.
+
+## Concave-Convex Growth
+
+- RKHS functions: capital `k`, consumption `c`, costate `mu`.
+- Algebraic helpers: diagnostic production power `z`, output `Y`, and marginal
+  product `P` returned after the solve.
+- Objective: `||k||_H^2 + ||c||_H^2 + ||mu||_H^2`.
+- Constraints: same economic equations as basic growth with production replaced
+  by `A max(k^a, b_1 k^a - b_2)`. JAX traces the max production function and its
+  marginal product directly; the solver does not use steady states, basin
+  thresholds, or branch enumeration. Residuals are checked on the collocation
+  grid and a denser validation grid; ambiguous crossing/local-solve failures
+  are rejected quickly rather than silently plotted.
+- Solver implementation: thin public wrapper around `neoclassical_growth_matern`
+  with kinked production parameters.
+
+## Human Capital
+
+- RKHS functions: physical capital `k`, human capital `h`, physical investment
+  `i_k`, human investment `i_h`, consumption `c`, and costates `mu_k`, `mu_h`.
+- Algebraic helpers: none.
+- Objective: sum of all seven squared RKHS norms.
+- Constraints: two accumulation equations, two Euler equations, resource
+  feasibility, `mu_k*c = 1`, and `mu_k = mu_h`.
+- Solver implementation: direct JAX/UNO nonlinear model with the small
+  initial-condition system solved in JAX through `nlls_gram`.
+
+## Optimal Advertising
+
+- RKHS functions: market share `x`, costate `mu`, advertising control `u`.
+- Algebraic helpers: none.
+- Objective: `||x||_H^2 + ||mu||_H^2 + ||u||_H^2`.
+- Constraints: market-share dynamics, costate equation, advertising marginal
+  condition, and positive control guard `u >= 1e-8`.
+- Solver implementation: direct JAX/UNO nonlinear model including the RKHS norm
+  for the kernel-represented control.