3 citations · 7 across the 7 of their papers we have counts for
7 papers
Scalable Derivative-Free Optimization Algorithms with Low-Dimensional Subspace Techniques
Zaikun Zhang
We re-introduce a derivative-free subspace optimization framework originating from Chapter 5 of the Ph.D. thesis [Z. Zhang, On Derivative-Free Optimization Methods, Ph.D. thesis, C…
PDFO: A Cross-Platform Package for Powell's Derivative-Free Optimization Solvers
Tom M. Ragonneau, Zaikun Zhang
The late Professor M. J. D. Powell devised five trust-region methods for derivative-free optimization, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. He carefully implemented t…
An Optimal Interpolation Set for Model-Based Derivative-Free Optimization Methods
Tom M. Ragonneau, Zaikun Zhang
This paper demonstrates the optimality of an interpolation set employed in derivative-free trust-region methods. This set is optimal in the sense that it minimizes the constant of…
Tight Error Bounds for the Sign-Constrained Stiefel Manifold
Xiaojun Chen, Yifan He, Zaikun Zhang
The sign-constrained Stiefel manifold in is a segment of the Stiefel manifold with fixed signs (nonnegative or nonpositive) for some columns of the matrice…
Polyhedron under Linear Transformations
Zaikun Zhang
The image and the inverse image of a polyhedron under a linear transformation are polyhedrons.
Notes on the Sobolev (Semi)Norms of Quadratic Functions
Zaikun Zhang
This paper studies the norm and seminorm of quadratic functions. The (semi)norms are expressed explicitly in terms of the coefficients of the quadratic function under c…
Sobolev Seminorm of Quadratic Functions with Applications to Derivative-Free Optimization
Zaikun Zhang
This paper studies the Sobolev seminorm of quadratic functions. The research is motivated by the least-norm interpolation that is widely used in derivative-free optimization.…