Solving Minimax Problems with Bilinear Objectives with ADMM
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908987492925440 |
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| author | Wilson, Bob |
| author_facet | Wilson, Bob |
| contents | We consider minimax (saddle-point) problems of the form max_{c \in C} min_{β\in S} g(c; β), where C and S are compact convex sets, and g is concave-convex. Applying the Alternating Direction Method of Multipliers (ADMM) requires evaluating a proximal operator that is, in general, as hard as the original problem. We show that when the outcome function g is bilinear, i.e. g(c; β) = c^T A β, the proximal operator reduces to a generalized projection onto the confidence region S. This reduction is exact -- it involves no approximation or linearization. The resulting ADMM algorithm alternates between (i) a generalized projection onto S and (ii) a Euclidean projection onto C. We describe the derivation, state the algorithm, and discuss convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20832 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solving Minimax Problems with Bilinear Objectives with ADMM Wilson, Bob Optimization and Control Methodology We consider minimax (saddle-point) problems of the form max_{c \in C} min_{β\in S} g(c; β), where C and S are compact convex sets, and g is concave-convex. Applying the Alternating Direction Method of Multipliers (ADMM) requires evaluating a proximal operator that is, in general, as hard as the original problem. We show that when the outcome function g is bilinear, i.e. g(c; β) = c^T A β, the proximal operator reduces to a generalized projection onto the confidence region S. This reduction is exact -- it involves no approximation or linearization. The resulting ADMM algorithm alternates between (i) a generalized projection onto S and (ii) a Euclidean projection onto C. We describe the derivation, state the algorithm, and discuss convergence. |
| title | Solving Minimax Problems with Bilinear Objectives with ADMM |
| topic | Optimization and Control Methodology |
| url | https://arxiv.org/abs/2604.20832 |