The impact of Lagrange-type functions on the efficiency of solution methods in non-convex optimization
- Authors: Giri, Jason
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at ICOTA6-2004, Ballarat, Australia : December
- Full Text:
- Reviewed:
- Description: The field of constrained non-linear optimization is one of the most practically applicable areas of mathematics. It has been used successfully to solve problems in a wide range of areas including economics, communications and computational chemistry. In recent years some problem reformulation techniques have been suggested for dealing with non-convex problems. However most of this study has been of a theoretical nature and very little is known about its effect on the practical impact of these techniques. In this seminar we will outline some of the reformulation techniques which have been suggested and present numerical results which show their relative efficiencies in solving some test problems. We will ultimately suggest that a reformulation scheme which combines a logarithmic reformulation of the objective function and an exponential reformulation of the constraint function provides many desirable outcomes.
- Description: E1
- Description: 2003000877
- Authors: Giri, Jason
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at ICOTA6-2004, Ballarat, Australia : December
- Full Text:
- Reviewed:
- Description: The field of constrained non-linear optimization is one of the most practically applicable areas of mathematics. It has been used successfully to solve problems in a wide range of areas including economics, communications and computational chemistry. In recent years some problem reformulation techniques have been suggested for dealing with non-convex problems. However most of this study has been of a theoretical nature and very little is known about its effect on the practical impact of these techniques. In this seminar we will outline some of the reformulation techniques which have been suggested and present numerical results which show their relative efficiencies in solving some test problems. We will ultimately suggest that a reformulation scheme which combines a logarithmic reformulation of the objective function and an exponential reformulation of the constraint function provides many desirable outcomes.
- Description: E1
- Description: 2003000877
Non-linear analogues of Lagrange functions in constrained optimization
- Authors: Giri, Jason
- Date: 2005
- Type: Text , Thesis , PhD
- Full Text:
- Description: "This thesis investigates several non-linear analogues of Lagrange functions in the hope of answering the question 'Is it possible to generalise Lagrange functions such that they may be applied to a range of nonconvex objective problems?' The answer to this question is found to be yes for a particular class of optimization problems. Furthermore the thesis asserts that in derivative free optimization the general schema which is most theoretically and practically appealing involves the reformulation of both objective and constraint functions, whilst the least practically successful approach for everything but the most simple convex case is the augmented Lagrangian approach."
- Description: Doctor of Philosophy
- Authors: Giri, Jason
- Date: 2005
- Type: Text , Thesis , PhD
- Full Text:
- Description: "This thesis investigates several non-linear analogues of Lagrange functions in the hope of answering the question 'Is it possible to generalise Lagrange functions such that they may be applied to a range of nonconvex objective problems?' The answer to this question is found to be yes for a particular class of optimization problems. Furthermore the thesis asserts that in derivative free optimization the general schema which is most theoretically and practically appealing involves the reformulation of both objective and constraint functions, whilst the least practically successful approach for everything but the most simple convex case is the augmented Lagrangian approach."
- Description: Doctor of Philosophy
Making statistics relevant for undergraduate nurses
- Martin, Peter, Pierce, Robyn, Giri, Jason
- Authors: Martin, Peter , Pierce, Robyn , Giri, Jason
- Date: 2002
- Type: Text , Conference paper
- Relation: Paper presented at the Sixth International Conference on Teaching Statistics, Cape Town, South Africa 7th - 12th July, 2002
- Full Text:
- Reviewed:
- Description: In this paper we will explore the challenge of making statistics more meaningful to future nurses. In the fast moving undergraduate student world the expectations we place upon nursing students are considerable. Typically they experience high class-contact hours in addition to their clinical placements. Compounding the problem, undergraduate nursing students have diverse mathematical backgrounds and seldom perceive statistics as being relevant for them. Given these constraints we have adopted the relatively modest aim of producing informed and discriminating consumers of statistics and research, rather than skilled statistical practitioners or researchers. With a focus on computer output rather than by-hand calculations, we have made use of strategic examples, appropriate journal articles and an historical hypothetical. This approach has both relieved the anxiety and distraction associated with calculations and increased students’ engagement in the learning process.
- Description: E1
- Description: 2003000142
- Authors: Martin, Peter , Pierce, Robyn , Giri, Jason
- Date: 2002
- Type: Text , Conference paper
- Relation: Paper presented at the Sixth International Conference on Teaching Statistics, Cape Town, South Africa 7th - 12th July, 2002
- Full Text:
- Reviewed:
- Description: In this paper we will explore the challenge of making statistics more meaningful to future nurses. In the fast moving undergraduate student world the expectations we place upon nursing students are considerable. Typically they experience high class-contact hours in addition to their clinical placements. Compounding the problem, undergraduate nursing students have diverse mathematical backgrounds and seldom perceive statistics as being relevant for them. Given these constraints we have adopted the relatively modest aim of producing informed and discriminating consumers of statistics and research, rather than skilled statistical practitioners or researchers. With a focus on computer output rather than by-hand calculations, we have made use of strategic examples, appropriate journal articles and an historical hypothetical. This approach has both relieved the anxiety and distraction associated with calculations and increased students’ engagement in the learning process.
- Description: E1
- Description: 2003000142
Changes of names, contents and attitudes to mathematical units
- Turville, Christopher, Pierce, Robyn, Barker, Ewan, Giri, Jason
- Authors: Turville, Christopher , Pierce, Robyn , Barker, Ewan , Giri, Jason
- Date: 2002
- Type: Text , Conference paper
- Relation: Paper presented at the 2nd International Conference on the Teaching of Mathematics, Crete, Greece : 1st June, 2003
- Full Text:
- Reviewed:
- Description: Will this material be on the exam? Why do I need to know this stuff? These are the sorts of questions that have been regularly asked by our mathematics students. Pre-service mathematics teachers often suggest that they do not need to learn anything that they do not have to teach. Generally, these students appear to have very little aesthetic appreciation for mathematics and its applications. Currently, we teach five traditional mathematical content units that are provided mainly for pre-service mathematics teachers. These units have been adapted and modified over the years from units that were designed primarily for science students. They contained a heavy focus on calculus with a limited breadth of mathematical experience. After consulting widely on the best mathematical practices throughout Australia and internationally, it was decided to reform all of the mathematics units to make them more attractive to a wider audience. The units that are currently being developed are: Profit, Loss and Gambling; Upon the Shoulders of Giants; Logic and Imagination; Modelling and Change; Algorithms, Bits and Bytes; Space, Shape, and Design; and Modelling Reality. The overall goal of this redevelopment is to improve student attitudes and motivation by exposing them to a wide range of topics in mathematics that are usable and relevant. All of these units will incorporate current technology, contain realistic problems, and include visiting speakers. Student assessment in these units will consist of portfolios, projects and examinations. The introduction of these new units will result in students having a greater choice of the units they wish to study. In order to overcome potential logistical problems of a small mathematics department, innovative changes to the structure of the units will also be examined. This paper will provide the details of the establishment and content of these units.
- Description: E1
- Description: 2003000085
- Authors: Turville, Christopher , Pierce, Robyn , Barker, Ewan , Giri, Jason
- Date: 2002
- Type: Text , Conference paper
- Relation: Paper presented at the 2nd International Conference on the Teaching of Mathematics, Crete, Greece : 1st June, 2003
- Full Text:
- Reviewed:
- Description: Will this material be on the exam? Why do I need to know this stuff? These are the sorts of questions that have been regularly asked by our mathematics students. Pre-service mathematics teachers often suggest that they do not need to learn anything that they do not have to teach. Generally, these students appear to have very little aesthetic appreciation for mathematics and its applications. Currently, we teach five traditional mathematical content units that are provided mainly for pre-service mathematics teachers. These units have been adapted and modified over the years from units that were designed primarily for science students. They contained a heavy focus on calculus with a limited breadth of mathematical experience. After consulting widely on the best mathematical practices throughout Australia and internationally, it was decided to reform all of the mathematics units to make them more attractive to a wider audience. The units that are currently being developed are: Profit, Loss and Gambling; Upon the Shoulders of Giants; Logic and Imagination; Modelling and Change; Algorithms, Bits and Bytes; Space, Shape, and Design; and Modelling Reality. The overall goal of this redevelopment is to improve student attitudes and motivation by exposing them to a wide range of topics in mathematics that are usable and relevant. All of these units will incorporate current technology, contain realistic problems, and include visiting speakers. Student assessment in these units will consist of portfolios, projects and examinations. The introduction of these new units will result in students having a greater choice of the units they wish to study. In order to overcome potential logistical problems of a small mathematics department, innovative changes to the structure of the units will also be examined. This paper will provide the details of the establishment and content of these units.
- Description: E1
- Description: 2003000085
CAS : Student engagement requires unambiguous advantages
- Pierce, Robyn, Herbert, Sandra, Giri, Jason
- Authors: Pierce, Robyn , Herbert, Sandra , Giri, Jason
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at 27th annual conference of the Mathematics Education Group of Australasia, Townsville, Australia : p. 462-469
- Full Text:
- Reviewed:
- Description: E1
- Description: 2003000921
- Authors: Pierce, Robyn , Herbert, Sandra , Giri, Jason
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at 27th annual conference of the Mathematics Education Group of Australasia, Townsville, Australia : p. 462-469
- Full Text:
- Reviewed:
- Description: E1
- Description: 2003000921
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