10 citations · 27 across the 17 of their papers we have counts for
18 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 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…
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…
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…
Exact penalty method for D-stationary point of nonlinear optimization
Xin-Wei Liu, Yu-Hong Dai
We consider the nonlinear optimization problem with least -norm measure of constraint violations and introduce the concepts of the D-stationary point, the DL-stationary poi…
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…
A primal-dual majorization-minimization method for large-scale linear programs
Xin-Wei Liu, Yu-Hong Dai, Ya-Kui Huang
We present a primal-dual majorization-minimization method for solving large-scale linear programs. A smooth barrier augmented Lagrangian (SBAL) function with strict convexity for t…
A novel augmented Lagrangian method of multipliers for optimization with general inequality constraints
Xin-Wei Liu, Yu-Hong Dai, Ya-Kui Huang +1
We introduce a twice differentiable augmented Lagrangian for nonlinear optimization with general inequality constraints and show that a strict local minimizer of the original probl…
A variable metric mini-batch proximal stochastic recursive gradient algorithm with diagonal Barzilai-Borwein stepsize
Tengteng Yu, Xin-Wei Liu, Yu-Hong Dai +1
Variable metric proximal gradient methods with different metric selections have been widely used in composite optimization. Combining the Barzilai-Borwein (BB) method with a diagon…
Equipping Barzilai-Borwein method with two dimensional quadratic termination property
Yakui Huang, Yu-Hong Dai, Xin-Wei Liu
A novel gradient stepsize is derived at the motivation of equipping the Barzilai-Borwein (BB) method with two dimensional quadratic termination property. A remarkable feature of th…
A primal-dual interior-point relaxation method with global and rapidly local convergence for nonlinear programs
Xin-Wei Liu, Yu-Hong Dai, Ya-Kui Huang
Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel primal-dual interior-point relaxat…
On the acceleration of the Barzilai-Borwein method
Yakui Huang, Yu-Hong Dai, Xin-Wei Liu +1
The Barzilai-Borwein (BB) gradient method is efficient for solving large-scale unconstrained problems to the modest accuracy and has a great advantage of being easily extended to s…
On the asymptotic convergence and acceleration of gradient methods
Yakui Huang, Yu-Hong Dai, Xin-Wei Liu +1
We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special instances. It is proved that each me…
Gradient methods exploiting spectral properties
Yakui Huang, Yu-Hong Dai, Xin-Wei Liu +1
We propose a new stepsize for the gradient method. It is shown that this new stepsize will converge to the reciprocal of the largest eigenvalue of the Hessian, when Dai-Yang's asym…
A family of spectral gradient methods for optimization
Yu-Hong Dai, Yakui Huang, Xin-Wei Liu
We propose a family of spectral gradient methods, whose stepsize is determined by a convex combination of the long Barzilai-Borwein (BB) stepsize and the short BB stepsize. Each me…
A primal-dual interior-point relaxation method for nonlinear programs
Xin-Wei Liu, Yu-Hong Dai
We prove that the classic logarithmic barrier problem is equivalent to a particular logarithmic barrier positive relaxation problem with barrier and scaling parameters. Based on th…
A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs
Yu-Hong Dai, Xin-Wei Liu, Jie Sun
With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmic-barrier problems of nonlinear programs.…