2 citations · 4 across the 10 of their papers we have counts for
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A Homogeneous Tensor Framework for High-Order Trust-Region and Spherical Polynomial Optimization
Wenqi Zhu, Haibin Chen, Guanglu Zhou
High-order methods can improve worst-case evaluation complexity, but for orders their Taylor subproblems are nonconvex polynomial optimization problems and are generally d…
A Globally Convergent Third-Order Newton Method via Unified Semidefinite Programming Subproblems
Yubo Cai, Wenqi Zhu, Coralia Cartis +1
We propose the Adaptive Levenberg-Marquardt Third-Order Newton Method (ALM-TON) method for unconstrained nonconvex optimization; to our knowledge, the framework provides the first…
Sufficiently Regularized Nonnegative Quartic Polynomials are Sum-of-Squares
Wenqi Zhu, Coralia Cartis
A polynomial that is nonnegative need not be a sum of squares of polynomials. This classical gap, identified by Hilbert in 1888, lies at the heart of why the global optimization of…
Global Optimality Characterizations and Algorithms for Minimizing Quartically-Regularized Third-Order Taylor Polynomials
Wenqi Zhu, Coralia Cartis
High-order methods for convex and nonconvex optimization, particularly th-order Adaptive Regularization Methods (AR), have attracted significant research interest by naturall…
Efficient Implementation of Third-Order Tensor Methods with Adaptive Regularization for Unconstrained Optimization
Coralia Cartis, Raphael Hauser, Yang Liu +2
High-order tensor methods that employ local Taylor models of degree within adaptive regularization frameworks (AR) have recently received significant attention, due to their…
Global Convergence of High-Order Regularization Methods with Sums-of-Squares Taylor Models
Wenqi Zhu, Coralia Cartis
High-order tensor methods that employ Taylor-based local models (of degree ) within adaptive regularization frameworks have been recently proposed for both convex and nonco…
Cubic-quartic regularization models for solving polynomial subproblems in third-order tensor methods
Wenqi Zhu, Coralia Cartis
High-order tensor methods for solving both convex and nonconvex optimization problems have generated significant research interest, leading to algorithms with optimal global rates…