Admin Only

GlobalView

Add to Quick Collection All 43 Results

Add All Items to Quick Collection

**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:**
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Aubin property | Calmness | Directional limiting coderivative | Solution map | Software engineering | Aubin properties | Fine analysis | Implicit function | Implicit multifunctions | Lipschitzian | Nocv1 | Polyhedral set | Computer science
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154327
**Description:** This paper is devoted to the development of new sufficient conditions for the calmness and the Aubin property of implicit multifunctions. As the basic tool we employ the directional limiting coderivat... More
**Full Text:**
**Reviewed:**
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Sum and pointwise supremum of convex functions | Fenchel and approximate subdifferentials
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154567
**Description:** We give a formula for the subdifferential of the sum of two convex functions where one of them is the supremum of an arbitrary family of convex functions. This is carried out under a weak assumption e... More
**Full Text:**
**Reviewed:**
**Date:** 2015
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Metric regularity | Induction theorem | Ekeland variational principle | Optimality conditions
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100394
**Description:** A general nonlinear regularity model for a set-valued mapping F : X x R+ paired right arrows Y, where X and Y are metric spaces, is studied using special iteration procedures, going back to Banach, Sc... More
**Full Text:**
**Reviewed:**
**Date:** 2015
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0802 Computation Theory and Mathematics | Error bound property | Generalized equations | Perturbation stability | Relative/directional metric regularity | Semicontinuous envelope | Directional metric regularity | Distance functions | Error bound | Generalized Equations | Lower semicontinuous | Metric regularity | Semi-continuous | Set-valued mapping | Mapping
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/98984
**Description:** In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming ... More
**Full Text:**
**Reviewed:**
**Authors:**
Kruger, Alexander
**Date:** 2015
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Calmness | Error bounds | Metric regularity | Metric subregularity | Slope
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/76402
**Description:** Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a... More
**Full Text:**
**Reviewed:**
**Date:** 2015
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Constrained polynomial programming | Problem | Necessary global optimality condition | Linear
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/92549
**Description:** The general constrained polynomial programming problem (GPP) is considered in this paper. Problem (GPP) has a broad range of applications and is proved to be NP-hard. Necessary global optimality condi... More
**Full Text:**
**Reviewed:**
**Date:** 2015
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0906 Electrical and Electronic Engineering | Collections of sets | Metric regularity | Normal cone | Subdifferential
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/92572
**Description:** Several primal and dual quantitative characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections... More
**Full Text:**
**Reviewed:**
**Date:** 2015
**Subject:** Conic programming | Generalized differentiation | Isolated calmness | Optimality conditions | Second-order theory | Tilt stability | Variational analysis | 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/77111
**Description:** This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a second-order generalized diff... More
**Full Text:**
**Reviewed:**
**Date:** 2014
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Constrained global optimization | Genetic algorithm | Hooke-Jeeves method | Hybrid method | Penalty function method
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/57007
**Description:** A new global optimization method combining genetic algorithm and Hooke-Jeeves method to solve a class of constrained optimization problems is studied in this paper. We first introduce the quadratic pe... More
**Full Text:**
**Reviewed:**
**Date:** 2014
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Calmness modulus | Isolated calmness | Linear programming | Semi-infinite programming | Variational analysis | Computer science | Software engineering | Constrained problem | Linear semi-infinite optimizations | Objective functions | Semi infinite programming | Semi-infinite programs | Mapping
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/44315
**Description:** Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective fun... More
**Full Text:**
**Reviewed:**
**Authors:**
Roshchina, Vera
**Date:** 2014
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Facially exposed cone | Nice cone | Pataki's conjecture | Software engineering | Nice cones | Computer science
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/45453
**Description:** We address the conjecture proposed by GÃ¡bor Pataki that every facially exposed cone is nice. We show that the conjecture is true in the three-dimensional case; however, there exists a four-dimensiona... More
**Full Text:**
**Reviewed:**
**Date:** 2014
**Subject:** Farkas lemma | Hahn-Banach theorem | Hahn-Banach-Lagrange theorem | Mazur-Orlicz theorem | 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/63117
**Description:** This paper provides new versions of the Farkas lemma characterizing those inequalities of the form f(x) â‰¥ 0 which are consequences of a composite convex inequality (S Â° g)(x) â‰¤ 0 on a closed conv... More
**Full Text:**
**Reviewed:**
**Date:** 2014
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Coderivatives | Full stability of local minimizers | Nondegeneracy | Quadratic growth | Second-order cone programming | Second-order subdifferentials | Strong regularity | Variational analysis | Optimal systems | Local minimizer | Stability
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/76551
**Description:** The paper presents complete characterizations of Lipschitzian full stability of locally optimal solutions to second-order cone programs (SOCPs) expressed entirely in terms of their initial data. These... More
**Full Text:**
**Reviewed:**

Second-order variational analysis in conic programming with applications to optimality and stability