Penalty-based first-order methods find ε-KKT points in bilevel minimax problems with Õ(ε^{-4}) deterministic and Õ(ε^{-9}) stochastic oracle complexity, improving prior bounds for constrained lower-level cases via Lagrangian duality.
First-order penalty methods for bilevel optimization.SIAM Journal on Optimization, 34(2):1937–1969
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Workshop notes explain models, subproblems, globalization, and convergence assumptions for PIPA, monotone-LCP PIPA, implicit-programming, and PSQP algorithms applied to MPECs.
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Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problems
Penalty-based first-order methods find ε-KKT points in bilevel minimax problems with Õ(ε^{-4}) deterministic and Õ(ε^{-9}) stochastic oracle complexity, improving prior bounds for constrained lower-level cases via Lagrangian duality.
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Optimization Workshop Notes for Mathematical Programming with Equilibrium Constraints Algorithms: Penalty Interior-Point, Implicit-Programming, and Piecewise SQP
Workshop notes explain models, subproblems, globalization, and convergence assumptions for PIPA, monotone-LCP PIPA, implicit-programming, and PSQP algorithms applied to MPECs.