First-Order Geometry, Spectral Compression, and Structural Compatibility under Bounded Computation
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which computational or feasibility limitations are encoded by self-adjoint operators defining locally reachable subspaces. In this setting, the optimal first-order improvement direction emerges as a pseudoinverse-weighted gradient, revealing how constraints induce a distorted ascent geometry. We further demonstrate that effective dynamics concentrate along dominant spectral modes, yielding a principled notion of spectral compression, and establish a compatibil...
| Authors | Changkai Li |
|---|---|
| Primary category | math.OC |
| Published | 9 March 2026 |
| Last updated at source | 9 March 2026 |
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