Hyper-Adaptive Momentum Dynamics for Native Cubic Portfolio Optimization: Avoiding Quadratization Distortion in Higher-Order Cardinality-Constrained Search
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917348758257664 |
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| author | Serbarinov, Greg |
| author_facet | Serbarinov, Greg |
| contents | We study cubic cardinality-constrained portfolio optimization, a higher-order extension of the standard Markowitz formulation where three-way sector co-movement terms augment the quadratic risk-return objective. Classical heuristics like simulated annealing (SA) and tabu search require Rosenberg quadratization of these cubic interactions. This inflates the variable count from n to 5n and introduces penalty terms that substantially distort the augmented search landscape. In contrast, Hyper-Adaptive Momentum Dynamics (HAMD) operates directly on the native higher-order objective using a hybrid pipeline combining continuous Hamiltonian search, exact cardinality-preserving projection, and iterated local search (ILS). On a cubic portfolio benchmark under matched 60-second CPU budgets, HAMD achieves substantially lower decoded native cubic objective values than SA and tabu search, yielding single-seed relative improvements of 87.9%, 71.2%, 59.5%, and 46.9% at n = 200, 300, 500, and 1000. In a detailed three-seed study at n = 200, HAMD attains a median native objective of 195.65 (zero variance), while SA and tabu yield 1208.07. Decoded-feasibility analysis shows SA satisfies all exact cardinality and Rosenberg auxiliary constraints, yet decodes to a native objective 80-88% worse than HAMD, demonstrating a surrogate-distortion effect rather than simple infeasibility. Exact calibration on small instances (n = 20, 25, 30) confirms HAMD finds the provably global optimum in 9/9 trials. These results demonstrate that native higher-order search offers a substantial advantage over quadratized surrogate optimization for constrained cubic portfolio problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15947 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hyper-Adaptive Momentum Dynamics for Native Cubic Portfolio Optimization: Avoiding Quadratization Distortion in Higher-Order Cardinality-Constrained Search Serbarinov, Greg Computational Finance Mathematical Finance Portfolio Management Risk Management 90C09, 90C59, 91G10 G.1.6; I.2.8; G.2.1; J.4 We study cubic cardinality-constrained portfolio optimization, a higher-order extension of the standard Markowitz formulation where three-way sector co-movement terms augment the quadratic risk-return objective. Classical heuristics like simulated annealing (SA) and tabu search require Rosenberg quadratization of these cubic interactions. This inflates the variable count from n to 5n and introduces penalty terms that substantially distort the augmented search landscape. In contrast, Hyper-Adaptive Momentum Dynamics (HAMD) operates directly on the native higher-order objective using a hybrid pipeline combining continuous Hamiltonian search, exact cardinality-preserving projection, and iterated local search (ILS). On a cubic portfolio benchmark under matched 60-second CPU budgets, HAMD achieves substantially lower decoded native cubic objective values than SA and tabu search, yielding single-seed relative improvements of 87.9%, 71.2%, 59.5%, and 46.9% at n = 200, 300, 500, and 1000. In a detailed three-seed study at n = 200, HAMD attains a median native objective of 195.65 (zero variance), while SA and tabu yield 1208.07. Decoded-feasibility analysis shows SA satisfies all exact cardinality and Rosenberg auxiliary constraints, yet decodes to a native objective 80-88% worse than HAMD, demonstrating a surrogate-distortion effect rather than simple infeasibility. Exact calibration on small instances (n = 20, 25, 30) confirms HAMD finds the provably global optimum in 9/9 trials. These results demonstrate that native higher-order search offers a substantial advantage over quadratized surrogate optimization for constrained cubic portfolio problems. |
| title | Hyper-Adaptive Momentum Dynamics for Native Cubic Portfolio Optimization: Avoiding Quadratization Distortion in Higher-Order Cardinality-Constrained Search |
| topic | Computational Finance Mathematical Finance Portfolio Management Risk Management 90C09, 90C59, 91G10 G.1.6; I.2.8; G.2.1; J.4 |
| url | https://arxiv.org/abs/2603.15947 |