Zobrazeno 1 - 10
of 127
pro vyhledávání: '"Gao, David Yang"'
Autor:
Gao, David Yang
A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer nonlinear optimization governed by linear and quadratic knapsack problems. It shows that the challenging knapsack problems can be solved analytically in ter
Externí odkaz:
http://arxiv.org/abs/1811.10130
Autor:
Gao, David Yang, Ali, Elaf Jaafar
This paper demonstrates a mathematically correct and computationally powerful method for solving 3D topology optimization problems. This method is based on canonical duality theory (CDT) developed by Gao in nonconvex mechanics and global optimization
Externí odkaz:
http://arxiv.org/abs/1803.02615
Autor:
Ruan, Ning, Gao, David Yang
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness is discus
Externí odkaz:
http://arxiv.org/abs/1801.08651
Autor:
Gao, David Yang
Topology optimization for general materials is correctly formulated as a bi-level knapsack problem, which is considered to be NP-hard in global optimization and computer science. By using canonical duality theory (CDT) developed by the author, the li
Externí odkaz:
http://arxiv.org/abs/1712.02919
Autor:
Gao, David Yang
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer nonlinear program
Externí odkaz:
http://arxiv.org/abs/1612.05684
Autor:
Lu, Xiaojun, Gao, David Yang
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 nonlinear differential equation with either Dirichlet/Neumann or mixed bou
Externí odkaz:
http://arxiv.org/abs/1607.05803
Autor:
Lu, Xiaojun, Gao, David Yang
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. Based on the canonical duality method, the corresponding Euler--Lagran
Externí odkaz:
http://arxiv.org/abs/1607.03995
Autor:
Gao, David Yang
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include traditional d
Externí odkaz:
http://arxiv.org/abs/1605.05534
Autor:
Latorre, Vittorio, Gao, David Yang
This paper presents a new canonical duality methodology for solving general nonlinear dynamical systems. Instead of the conventional iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the leas
Externí odkaz:
http://arxiv.org/abs/1512.08343
Autor:
Gao, David Yang
This note is a response to recent challenge by showing basic mistakes in his conclusions. The proof is elementary, but leads to some fundamental results in correctly understanding an extensively studied problem in continuum mechanics.
Comment: F
Comment: F
Externí odkaz:
http://arxiv.org/abs/1511.03374