# Invariant 3.15 — Optimization under constraint / Pareto fronts

slug: oip-invariant-15-315-optimization-under-constraint-pareto-fronts · https://miscsubjects.com/a/oip-invariant-15-315-optimization-under-constraint-pareto-fronts · tags: philosophy, oip, catalogue, invariant, systems-theory · updated 2026-07-17T02:36:14.669Z

## 3.15 Optimization under constraint / Pareto fronts
Systems settle where no objective improves without another worsening. **Sources:** Pareto; linear programming; evolutionary trade-off theory; thermodynamic bounds. **Domains:** economics, biology, engineering, AI. **Dual:** unconstrained/infeasible. **Tier:** T0/T1. **Falsifier:** a stable system dominated on all objectives by a reachable alternative. **Maps:** A₂, A₃ (the triple optimum is a Pareto point).

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## Corpus map
- Same invariant, other planes: [Catalogue node C15](/a/oip-node-c15-optimization-under-constraint-pareto-fronts) · [Encyclopedia C15](/a/convergence-encyclopedia-c15)
- Inventory hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article)