Admin Only

GlobalView

Add to Quick Collection All 143 Results

Add All Items to Quick Collection

**Date:** 2017
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0802 Computation Theory and Mathematics | Nonsmooth optimization | Nonconvex optimization | Proximal bundle methods | DC functions | Cutting plane model
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/159321
**Description:** In this paper, we develop a version of the bundle method to solve unconstrained difference of convex (DC) programming problems. It is assumed that a DC representation of the objective function is avai... More
**Reviewed:**
**Date:** 2017
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0906 Electrical and Electronic Engineering | Polynomial splines | Chebyshev approximation | Free knots | Quasidifferential | Best approximation conditions
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/159295
**Description:** In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions of varying degree from one interval to another. Based on these results, we obtain a characteri... More
**Reviewed:**
**Date:** 2017
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Double well potential | Gener alized ginzburg-landau functional | Non-convex quadratic programming | Polynomial optimization
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/158335
**Description:** A special type of multi-variate polynomial of degree 4, called the double well potential function, is studied. It is derived from a discrete approx imation of the generalized Ginzburg-Landau functiona... More
**Reviewed:**
**Date:** 2017
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Non-convex quadratic programming | Polynomial optimization | Generalized Ginzburg-Landau functional | Double well potential
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/158516
**Description:** A special type of multi-variate polynomial of degree 4, called the double well potential function, is studied. It is derived from a discrete approximation of the generalized Ginzburg-Landau functional... More
**Reviewed:**
**Date:** 2017
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0906 Electrical and Electronic Engineering | Farkas-type theorems | Vector optimization | Weak solutions | Vector variational inequalities | Vector equilibrium problems
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/159226
**Description:** The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of s... More
**Reviewed:**
**Date:** 2017
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Canonical duality theory | D.C. programming | Global optimization | Mathematical modeling
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/104304
**Description:** This paper presents a canonical d.c. (difference of canonical and convex functions) programming problem, which can be used to model general global optimization problems in complex systems. It shows th... More
**Reviewed:**
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Vector optimization | Density theorem | Nonlinear separation theorem | Augmented dual cone | Proper efficiency
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/102050
**Description:** The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasin... More
**Reviewed:**
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Global optimization | Nonlinear constrained programming | Augmented Lagrangian
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154463
**Description:** This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is pro... More
**Reviewed:**
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0906 Electrical and Electronic Engineering | Uniform approximation | Polynomial splines | Alternance | Weighting functions
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154696
**Description:** In this paper, we derive conditions for best uniform approximation by fixed knots polynomial splines with weighting functions. The theory of Chebyshev approximation for fixed knots polynomial function... More
**Reviewed:**
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0906 Electrical and Electronic Engineering | Slope | Metric regularity | Holder metric regularity | Generalized equation | Frechet subdifferential | Asplund spaces | Ekeland variational principle | Hadamard directional differentiability
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154639
**Description:** This paper sheds new light on regularity of multifunctions through various characterizations of directional Holder/Lipschitz metric regularity, which are based on the concepts of slope and coderivativ... More
**Reviewed:**
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0913 Mechanical Engineering | Canonical duality theory | Chaos | Global optimization | Nonlinear dynamics | NP-hardness
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/102320
**Description:** This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated a... More
**Reviewed:**
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Canonical duality theory | CEC benchmark | Constrained optimization | Global optimization
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100713
**Description:** This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Based on canonical duality theory, these c... More
**Full Text:**
**Reviewed:**
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0802 Computation Theory and Mathematics | Canonical duality theory | Double-well function | Global optimization | Log-sum-exp function | Minimax problems | Polynomial minimisation
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100457
**Description:** This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of 4th-order polynomial and a log-sum-exp function. Such a problem arises extensivel... More
**Full Text:**
**Reviewed:**
**Authors:**
Kruger, Alexander
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0906 Electrical and Electronic Engineering | Error bounds, Slope | Metric regularity | Metric subregularity | Holder metric subregularity | Calmness
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154508
**Description:** In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the fra... More
**Reviewed:**
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0802 Computation Theory and Mathematics | Graphical Derivative | Mathematical Program With Equilibrium Constraints | Parameterized Generalized Equation | Regular Coderivative | Constraint theory | Mapping | Control constraint | Generalized derivatives | Generalized Equations | Inequality constraint | Qualification conditions | Strong stationarity | C (programming language)
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/104265
**Description:** The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the normal-cone mapping related to C2 inequality constraints under very weak qualification cond... More
**Reviewed:**