Strong Convergence of FISTA for Affinely Constrained Convex Quadratic Minimization
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914439421231104 |
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| author | Bartz, Sedi Bauschke, Heinz H. Gao, Yuan Moursi, Walaa M. |
| author_facet | Bartz, Sedi Bauschke, Heinz H. Gao, Yuan Moursi, Walaa M. |
| contents | In October 2025, research by Boţ, Fadili, and Nguyen, and by Jang and Ryu, led to the seminal result that Beck and Teboulle's FISTA converges weakly to a minimizer of the sum of two convex functions resolving a long-standing open problem. The first strong convergence result was obtained in November 2025 by Moursi, Naguib, Pavlovic, and Vavasis for affinely constrained convex minimization provided certain closedness conditions hold.
In this paper, we prove strong convergence in the affine-quadratic case without any closedness assumption. Specializing this to the unconstrained case, we obtain the strong convergence of Nesterov's accelerated gradient method when applied to a convex quadratic objective function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01636 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong Convergence of FISTA for Affinely Constrained Convex Quadratic Minimization Bartz, Sedi Bauschke, Heinz H. Gao, Yuan Moursi, Walaa M. Optimization and Control 5K05, 65K10, 90C20, 90C25 (Primary) 47H09 (Secondary) In October 2025, research by Boţ, Fadili, and Nguyen, and by Jang and Ryu, led to the seminal result that Beck and Teboulle's FISTA converges weakly to a minimizer of the sum of two convex functions resolving a long-standing open problem. The first strong convergence result was obtained in November 2025 by Moursi, Naguib, Pavlovic, and Vavasis for affinely constrained convex minimization provided certain closedness conditions hold. In this paper, we prove strong convergence in the affine-quadratic case without any closedness assumption. Specializing this to the unconstrained case, we obtain the strong convergence of Nesterov's accelerated gradient method when applied to a convex quadratic objective function. |
| title | Strong Convergence of FISTA for Affinely Constrained Convex Quadratic Minimization |
| topic | Optimization and Control 5K05, 65K10, 90C20, 90C25 (Primary) 47H09 (Secondary) |
| url | https://arxiv.org/abs/2604.01636 |