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Professor David Gao

Alexander Rubinov Professor of Mathematics

School of Engineering, IT and Phys. Sci.

Section/Portfolio:

Applied Mathematics

Location:

Mt Helen Campus, Online

Canonical Duality Theory and Algorithm for Solving Bilevel Knapsack Problems with Applications

A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer...

On modeling and complete solutions to general fixpoint problems in multi-scale systems with applications

This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical...

On SDP method for solving canonical dual problem in post buckling of large deformed elastic beam

This paper presents a new methodology and algorithm for solving post buckling problems of a large...

On topology optimization and canonical duality method

Topology optimization for general materials is correctly formulated as a bi-level knapsack...

Analytic Solutions to 3-D Finite Deformation Problems Governed by St Venant Kirchhoff Material

This paper presents a detailed study on analytical solutions to a general nonlinear...

Analytic Solutions to Large Deformation Problems Governed by Generalized Neo-Hookean Model

This paper addresses some fundamental issues in nonconvex analysis. By using pure complementary...

Canonical Dual Approach for Contact Mechanics Problems with Friction,

This paper presents an application of Canonical duality theory to the solution of contact...

Canonical Duality Method for Solving Kantorovich Mass Transfer Problem,

This paper addresses analytical solution to the Kantorovich mass transfer problem . Through an...

Canonical Duality Theory for Solving Nonconvex/Discrete Constrained Global Optimization Problems

This paper presents a canonical duality theory for solving general nonconvex/discrete constrained...

Canonical Duality Theory for Solving Non-Monotone Variational Inequality Problems

This paper presents a canonical dual approach for solving a class of non-monotone variational...

Canonical Duality Theory for Topology Optimization

This paper presents a canonical duality approach for solving a general topology optimization...

Canonical Duality Theory: Unified Methodology for Multidisciplinary Study

This book on canonical duality theory provides a comprehensive review of its philosophical...

Canonical Duality-Triality Theory: Bridge Between Nonconvex Analysis/Mechanics and Global Optimization in Complex System

Canonical duality-triality is a breakthrough methodological theory, which can be used not only...

Canonical Primal-Dual Method for Solving Nonconvex Minimization Problems

A new primal–dual algorithm is presented for solving a class of nonconvex minimization...

Double well potential function and its optimization in the n-dimensional real space - Part I

A special type of multi-variate polynomial of degree 4, called the double well potential...

Global Optimal Solution Computation of a Quadratic Integer Programming Problem with Linear Inequality Constraints

This paper presents a canonical dual method for solving a quadratic discrete value selection...

  • Book Chapters

Global Optimal Solution to Quadratic Discrete Programming Problem with Inequality Constraints

This paper presents a canonical dual method for solving a quadratic discrete value selection...

Global Solutions to Spherically Constrained Quadratic Minimization via Canonical Duality Theory

This paper presents a detailed study on global optimal solutions to a nonconvex quadratic...

Improved Canonical Dual Finite Element Method and Algorithm for Post-Buckling Analysis of Nonlinear Gao Beam

This paper deals a study on post-buckling problem of a large deformed elastic beam by using a...

On D.C. Optimization Problems

A canonical d.c. (difference of canonical and convex functions) programming problem is proposed,...

On Minimal Distance Between Two Surfaces,

This article corrects the results presented in [7] (D.Y. Gao and Wei-Chi, Yang, Optimization,...

On modeling and global solutions for d.c. optimization problems by canonical duality theory

This paper presents a canonical d.c. (difference of canonical and convex functions) programming...

On the Convexity of Nonlinear Elastic Energies in the Right Cauchy-Green Tensor

We present a sufficient condition under which a weak solution of the Euler-Lagrange equations in...

Remarks on Analytic Solutions and Ellipticity in Anti-plane Shear Problems of Nonlinear Elasticity

This paper revisits a well-studied anti-plane shear deformation problem formulated by Knowles in...

Triality Theory for General Unconstrained Global Optimization Problems,

Triality theory is proved for a general unconstrained global optimization problem. The method...

Analytical solutions to general anti-plane shear problems in finite elasticity

This paper presents a pure complementary energy variational method for solving a general...

Canonical duality for solving general nonconvex constrained problems

This paper presents a canonical duality theory for solving a general nonconvex constrained...

Canonical finite element method for solving nonconvex variational problems to post buckling beam problem

The goal of this paper is to solve the post buckling phenomena of a large deformed elastic beam...

Discrete state transition algorithm for unconstrained integer optimization problems

A recently new intelligent optimization algorithm called discrete state transition algorithm is...

Global Optimal Trajectory in Chaos and NP-Hardness

This paper presents an unconventional theory and method for solving general nonlinear dynamical...

Global solutions to a class of CEC benchmark constrained optimization problems

This paper aims to solve a class of CEC benchmark constrained optimization problems that have...

Global solutions to nonconvex optimization of 4th-order polynomial and log-sum-exp functions

This paper presents a canonical dual approach for solving a nonconvex global optimization problem...

On the extrema of a nonconvex functional with double-well potential in 1D

This paper mainly investigates the extrema of a nonconvex functional with double-well potential...

On unified modeling, theory, and method for solving multi-scale global optimization problems

A unified model is proposed for general optimization problems in multi-scale complex systems....

Optimal design of water distribution networks by a discrete state transition algorithm

In this study it is demonstrated that, with respect to model formulation, the number of linear...

RETRACTED:A framework of canonical dual algorithms for global optimization

[No abstract available]

RETRACTED: Triality theory and complete post-buckling solutions of large deformed beam by canonical dual finite element method (Mathematics and Mechanics of Solids)

[No abstract available]

RETRACTED:Unified canonical duality methodology for global optimization

[No abstract available]

Advances in Global Optimization

A multiobjective state transition algorithm for single machine scheduling

Application of canonical duality theory to fixed point problem

Canonical dual approach for minimizing a nonconvex quadratic function over a sphere

Canonical duality theory and triality for solving general global optimization problems in complex systems

General nonconvex optimization problems are studied by using the canonical duality-triality...

Dynamical analysis of neural networks with time-varying delays using the LMI approach

This study is concerned with the delay-range-dependent stability analysis for neural networks...

Editorial for special issue on methods of optimisation and their applications

Objectives: National dietary guidelines were introduced in 1977 and 1983, by the US and UK...

  • Journals

Global solutions to fractional programming problem with ratio of nonconvex functions

This paper presents a canonical dual approach for minimizing a sum of quadratic function and a...

Intuitive haptics interface with accurate force estimation and reflection at nanoscale

Machine learning in intelligent video and automated monitoring

[No abstract available]

Mixed finite element solutions to contact problems of nonlinear Gao beam on elastic foundation

This paper analyzes nonlinear contact problems of a large deformed beam on an elastic foundation....

Model modification in scheduling of batch chemical processes

Preface to the Springer Proceedings in Mathematics and Statistics Volume 9

[No abstract available]

  • Journals

Canonical duality approach for non-linear dynamical systems

This paper presents a canonical dual approach for solving a non-linear population growth problem...

Canonical dual solutions to nonconvex radial basis neural network optimization problem

Radial Basis Functions Neural Networks (RBFNNs) are tools widely used in regression problems. One...

Canonical primal-dual algorithm for solving fourth-order polynomial minimization problems

This paper focuses on implementation of a general canonical primal-dual algorithm for solving a...

Global optimal solutions to general sensor network localization problem

Sensor network localization problem is to determine the position of the sensor nodes in a network...

Impulsive control for synchronizing delayed discrete complex networks with switching topology

In this paper, global exponential synchronization of a class of discrete delayed complex networks...

NP-Hard Problems in Computational Large Deformation Mechanics and Canonical Dual Finite Element Method

  • Conference Proceedings

Postbuckling analysis of a nonlinear beam with axial functionally graded material

The postbuckling analysis of a modified nonlinear beam composed of axial functionally graded...

Post-buckling solutions of hyper-elastic beam by canonical dual finite element method

The post-buckling problem of a large deformed beam is analyzed using the canonical dual finite...

Stable trajectory of logistic map

In this paper, the stable trajectory of Logistic Map has been investigated by canonical duality...

A Comparative study of state transition algorithm with harmony search and artificial bee colony

A direct optimization method for low group delay FIR filter design

This paper studies the design of FIR filter with low group delay, where the desired phase...

An efficient classification using support vector machines

  • Conference Proceedings

Canonical duality for radial basis neural networks

Radial Basis Function Neural Networks (RBF NN) are a tool largely used for regression problems....

COMPLETE SOLUTIONS AND TRIALITY THEORY TO A NONCONVEX OPTIMIZATION PROBLEM WITH DOUBLE-WELL POTENTIAL IN R-n

Solving the canonical dual of box- and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm

This paper presents a massively parallel global deterministic direct search method (VTDIRECT) for...

Video driven traffic modelling

Video driven traffic modelling in paramics

Anticipating synchronization through optimal feedback control

Applying the canonical dual theory in optimal control problems

Canonical dual approach to solving the maximum cut problem

Canonical dual finite element method for solving post-buckling problems of a large deformation elastic beam

This paper presents a canonical dual mixed finite element method for the post-buckling analysis...

Canonical duality theory and algorithm for solving challenging problems in network optimisation

Canonical dual solutions to sum of fourth-order polynomials minimization problems with applications to sensor network localization

Global minimizer of large scale stochastic rosenbrock function: canonical duality approach

Global optimal solutions to a class of quadrinomial minimization problems with one quadratic constraint

Global optimal solutions to nonconvex euclidean distance geometry problems

  • Conference Proceedings

Impulsive synchronization of state delayed discrete complex networks with switching topology

ON THE TRIALITY THEORY FOR A QUARTIC POLYNOMIAL OPTIMIZATION PROBLEM

This paper presents a detailed proof of the triality theorem for a class of fourth-order...

Preface - Journal of Global Optimization Vol54

[No abstract available]

A novel canonical dual computational approach for prion AGAAAAGA amyloid fibril molecular modeling

Many experimental studies have shown that the prion AGAAAAGA palindrome hydrophobic region...

Global optimization over a box via canonical dual function

In this paper, we study global concave optimization by the canonical dual function. A...

OPTIMIZATION OF MATRIX SEMIRINGS FOR CLASSIFICATION SYSTEMS

The max-plus algebra is well known and has useful applications in the investigation of discrete...

A study on concave optimization via canonical dual function

  • Journals

Canonical dual least square method for solving general nonlinear systems of quadratic equations

This paper presents a canonical dual approach for solving general nonlinear algebraic systems. By...

Canonical dual solutions for fixed cost quadratic programs

This chapter presents a canonical dual approach for solving a mixed-integer quadratic...

Global optimization by canonical dual function

In this paper, the canonical dual function (Gao, 2004 [4]) is used to solve a global...

Handbook of Nonconvex Analaysis and Applications

  • Book

Solutions to quadratic minimization problems with box and integer constraints

This paper presents a canonical duality theory for solving quadratic minimization problems...

An asymptotic expression of the Schrodinger equation

  • Journals

Canonical Dual Approach to Binary Factor Analysis

  • Conference Proceedings

Canonical duality for solving nonconvex and nonsmooth optimization problem

This paper presents an application of the canonical duality theory for solving a class of...

Canonical Duality Theory: Connections bewtween Nonconvex Mechanics and Global Optimization.

  • Book Chapters

Canonical duality theory: Unified understanding and generalized solution for global optimisation problems

Global optimization for a class of fractional programming problems

  • Journals

Solutions and optimality criteria for nonconvex constrained global optimization problems with connections between canonical and Lagrangian duality

This paper presents a canonical duality theory for solving a general nonconvex quadratic...

Solution to nonconvex quadratic programming with both inequality and box constraints

  • Journals

Traveling wave solutions to a reaction-diffusion equation

  • Journals

Advances in canonical duality theory with applications to global optimization.

  • Conference Proceedings

A nonconvex dissipative system and its applications (II)

  • Journals

Canonical dual approach to solving 0-1 quadratic programming problems

  • Journals

Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem

  • Journals

Global extremal conditions for multi-integer quadratic programming

  • Journals

Minimal distance between two non-convex surfaces

[No abstract available]

Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation

  • Journals

Multi-scale modelling and canonical dual finite element method in phase transitions of solids

  • Journals

Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem

This paper presents a set of complete solutions and optimality conditions for a nonconvex...

The Korteweg-de Vries-Burgers equation and its approximate solution

  • Journals

Computing lower and upper bounds on stress intensity factors in bimaterials

  • Journals

Solutions and optimality criteria to box constrained nonconvex minimization problems

  • Journals

Complete solutions and extremality criteria to polynominal optimization problems

  • Journals