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math.OC2025
A Surrogate Value Function Formulation for Bilevel Optimization
Mengwei Xu, Yu-Hong Dai, Xin-Wei Liu +1
The value function formulation captures the hierarchical nature of bilevel optimization through the optimal value function of the lower level problem, yet its implicit and nonsmoot…
math.OC2025
A Newton Augmented Lagrangian Method for Symmetric Cone Programming with Complexity Analysis
Rui-Jin Zhang, Ruoyu Diao, Xin-Wei Liu +1
Symmetric cone programming covers a broad class of convex optimization problems, including linear programming, second-order cone programming, and semidefinite programming. Although…
math.OC2025
Optimization over Trained Neural Networks: Difference-of-Convex Algorithm and Application to Data Center Scheduling
Xinwei Liu, Vladimir Dvorkin
When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approx…