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Newton-CG methods for nonconvex unconstrained optimization with Hölder continuous Hessian
Chuan He, Heng Huang, Zhaosong Lu
In this paper we consider a nonconvex unconstrained optimization problem minimizing a twice differentiable objective function with Hölder continuous Hessian. Specifically, we first…
A Parameter-Free Conditional Gradient Method for Composite Minimization under Hölder Condition
Masaru Ito, Zhaosong Lu, Chuan He
In this paper we consider a composite optimization problem that minimizes the sum of a weakly smooth function and a convex function with either a bounded domain or a uniformly conv…
A Newton-CG based augmented Lagrangian method for finding a second-order stationary point of nonconvex equality constrained optimization with complexity guarantees
Chuan He, Zhaosong Lu, Ting Kei Pong
In this paper we consider finding a second-order stationary point (SOSP) of nonconvex equality constrained optimization when a nearly feasible point is known. In particular, we fir…
A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization
Chuan He, Heng Huang, Zhaosong Lu
In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject…