6 papers · 1 filter
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…
Enhanced Barrier-Smoothing Technique for Bilevel Optimization with Nonsmooth Mappings
Mengwei Xu, Yu-Hong Dai, Xin-Wei Liu +1
Bilevel optimization problems, encountered in fields such as economics, engineering, and machine learning, pose significant computational challenges due to their hierarchical struc…
A mechanism of three-dimensional quadratic termination for the gradient method with applications
Yakui Huang, Yu-Hong Dai, Xin-Wei Liu
Recent studies show that the two-dimensional quadratic termination property has great potential in improving performance of the gradient method. However, it is not clear whether hi…