4 papers
Polynomial iteration complexity of a path-following smoothing Newton method for symmetric cone programming
Yu-Hong Dai, Ruoyu Diao, Xin-Wei Liu +1
It has long remained open whether smoothing Newton methods (SNMs) for symmetric cone programming (SCP) admit polynomial iteration complexity. A key difficulty lies in the lack of a…
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…
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…
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…