2 citations · 5 across the 7 of their papers we have counts for
7 papers
Multiple nonsmooth solutions for nonconvex variational boundary value problems in
Xiaojun Lu, David Yang Gao
This paper presents a set of complete solutions of a nonconvex variational problem with a double-well potential. Based on the canonical duality-triality theory, the associated nonl…
Canonical dual method for mixed integer fourth-order polynomial minimization problems with fixed cost terms
Zhong Jin, David Y Gao
We study a canonical duality method to solve a mixed-integer nonconvex fourth-order polynomial minimization problem with fixed cost terms. This constrained nonconvex problem can be…
On the extrema of a nonconvex functional with double-well potential in higher dimensions
Xiaojun Lu, David Yang Gao
This paper mainly addresses the extrema of a nonconvex functional with double-well potential in higher dimensions through the approach of nonlinear partial differential equations.…
Canonical Duality-Triality Theory: Bridge Between Nonconvex Analysis/Mechanics and Global Optimization in Complex Systems
David Y Gao, Ning Ruan, Vittorio Latorre
Canonical duality-triality is a breakthrough methodological theory, which can be used not only for modeling complex systems within a unified framework, but also for solving a wide…
Double Well Potential Function and Its Optimization in The n-dimensional Real Space -- Part I
Shu-Cherng Fang, David Yang Gao, Gang-Xuan Lin +2
A special type of multi-variate polynomial of degree 4, called the double well potential function, is studied. When the function is bounded from below, it has a very unique propert…
Canonical Duality Approach for Nonlinear Dynamical Systems
Ning Ruan, David Y. Gao
This paper presents a canonical dual approach for solving a nonlinear population growth problem governed by the well-known logistic equation. Using the finite difference and least…