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1Hyperfuzzy And SuperHyperfuzzy Extensions Of Linear Programming: Modelsand Mathematical Foundations

A fuzzy set assigns to each element of a universe a membership degree within the interval [0, 1], thereby modeling imprecision and vagueness. A hyperfuzzy set extends this concept by associating each element with a nonempty subset of [0, 1], capturing both uncertainty and variability through a range of possible membership degrees. Building on this, a superhyperfuzzy set generalizes the framework further by assigning to each nonempty element in the  n th power-set hierarchy a nonempty subset of [0, 1], thus enabling the representation of recursively structured and hierarchical uncertainty. Linear programming is an optimization technique that aims to maximize or minimize a linear objective function subject to a set of linear equality and inequality constraints. Fuzzy linear programming generalizes this framework by incorporating fuzzy numbers into the objective coefficients and constraints, allowing for uncertainty in both parameters and feasible regions. In this paper, we propose mathematical models for Hyperfuzzy Linear Programming and Superhyperfuzzy Linear Programming, and briefly examine their theoretical properties. We hope that these models will provide a foundation for further validation, development, and refinement in future research.

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2DTIC ADA203392: Nonprocedural Implementation Of Mathematical Programming Algorithms

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It is shown that the implementation of many mathematical programming algorithms using spreadsheet software can be described as instances of a nonprocedural approach to computer programming. This concept is generalized to an abstract computing environment called HYPERCELLS. Its significance in view of rapid development in parallel computation is discussed. With the widespread use of microcomputers in academia, business, industry and government, spreadsheet software has become the most popular general purpose quantitative tool for numerical computation. It is essentially a two dimensional array of cells. Each cell may contain text for documentation, numerical values from data, or a formula dependent on values in other cells. Whenever the value in a cell is changed, the content of cells with formulas depending on it can be recalculated automatically.

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3DTIC ADA450514: A Knowledge-Based Creation Of Mathematical Programming For GIS Problem Solving

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Nowadays the biggest challenge to GIS is the model design of theme analyzing. Many GIS applications need more functions in analysis and decision-making than in data organization or visualization. While confronted with an application like planning a new metro line in a city, the typical GIS cannot accomplish it by itself, unless some human experts or artificial intelligence technology are involved. Numbers of GIS applications essentially are models of theme analyzing, and they are also examples of problem solving in AI. Therefore many theories and technologies from AI can be embedded in GIS to strengthen its ability of automatic analysis. Fortunately mathematical programming is a kind of powerful tool to settle problems with a demand of optimization under some constraint conditions. Many GIS applications happen to be this type, and some mathematical models can usually approximate them accurately. Two new questions aroused. The first is what objective function and constraint conditions that constitute a mathematical programming should be, and the second is how to acquire those mathematical expressions. Due to the establishment of a mathematical programming is highly knowledge-based, so an AI subsystem is designed to autonomously create a mathematical programming. This problem has a typical characteristic of multiple domains crossing from perspective of Knowledge Engineering, so some novel knowledge-processing methods, like knowledge dependence, knowledge transition and knowledge reference, are studied. And a knowledge system represented by frames and a reference-based knowledge-using method are presented here.

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4DTIC ADA1004574: NETGEN-II: A System For Generating Structured Network-Based Mathematical Programming Test Problems,

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The increased importance of designing and implementing algorithms to solve particular management problems has created the need for more robust test problem generators that can match the overall structure and parameter values of these problems. Of particular interest are management problems that can be modeled using a network structure. This paper discussed the design of a system for generating network-based mathematical programming test problems that conform to user-supplied structural & parameter characteristics. (Author)

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5DTIC ADA116970: Soviet Mathematical Programming,

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Contents: Problem Definitions; Military Applications; Military Advocacy; Brief Chronology; Selected Specialists, and Implications and Future.

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6DTIC AD0400573: DYNAMIC PROGRAMMING AND MATHEMATICAL ECONOMICS

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Contents: Problem Definitions; Military Applications; Military Advocacy; Brief Chronology; Selected Specialists, and Implications and Future.

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7DTIC ADA299185: New Capabilities For Strategic Mobility Analysis Using Mathematical Programming.

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Contents: Problem Definitions; Military Applications; Military Advocacy; Brief Chronology; Selected Specialists, and Implications and Future.

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8DTIC ADA264091: Symposium On Applied Mathematical Programming And Modeling (APMOD93) Held In Budapest, Hungary On January 6-8, 1993. Volume Of Extended Abstracts

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Partial Contents: Implementing a Maximum Flow Algorithm; Experiments with Dynamic Trees; On Decomposition of Dual Variables in Linear Programming and its Economic Interpretation; Graph-Based Modeling with MIMI/G; Impact of Quantitative Methods on Logical Interference Problem; Scheduling Multiprocessors tasks on a Dynamic Configurations of Dedicated Processors

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9Mathematical Foundations Of Programming Language Semantics : 3rd Workshop, Tulane University, New Orleans, Louisiana, USA, April 8-10, 1987 : Proceedings

Partial Contents: Implementing a Maximum Flow Algorithm; Experiments with Dynamic Trees; On Decomposition of Dual Variables in Linear Programming and its Economic Interpretation; Graph-Based Modeling with MIMI/G; Impact of Quantitative Methods on Logical Interference Problem; Scheduling Multiprocessors tasks on a Dynamic Configurations of Dedicated Processors

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10Mathematical Programming And The Aircraft Squadron.

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Partial Contents: Implementing a Maximum Flow Algorithm; Experiments with Dynamic Trees; On Decomposition of Dual Variables in Linear Programming and its Economic Interpretation; Graph-Based Modeling with MIMI/G; Impact of Quantitative Methods on Logical Interference Problem; Scheduling Multiprocessors tasks on a Dynamic Configurations of Dedicated Processors

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11Readings In Mathematical Programming

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Partial Contents: Implementing a Maximum Flow Algorithm; Experiments with Dynamic Trees; On Decomposition of Dual Variables in Linear Programming and its Economic Interpretation; Graph-Based Modeling with MIMI/G; Impact of Quantitative Methods on Logical Interference Problem; Scheduling Multiprocessors tasks on a Dynamic Configurations of Dedicated Processors

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12A Critical Review Of Comparisons Of Mathematical Programming Algorithms And Software (1953-1977)

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Journal of Research of the National Bureau of Standards

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13Mathematical Programming With Business Applications

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Journal of Research of the National Bureau of Standards

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14Introduction To Mathematical Programming. Operations Research. Volume 1

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Journal of Research of the National Bureau of Standards

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15ERIC ED081230: A Course Which Used Programming To Aid Learning Various Mathematical Concepts.

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A three unit mathematics course entitled Introduction to Computing evaluated the effectiveness of programing as an aid to learning math concepts and to developing student self-reliance. Sixteen students enrolled in the course at the College of Notre Dame in Belmont, California; one terminal was available, connected to the Stanford Computation Center IBM 360/67, and the interactive mode and BASIC were used. Two texts were required--BASIC Manual and Notes for BASIC. Students solved two problems a week in algebra, calculus, or linear algebra for the first eight weeks, providing problem descriptions, flowcharts, program listings, sample outputs, conjectures, and conclusions. In the last half of the course each student completed a major individual project. The teacher lectured on programing concepts and BASIC in the early part of the course and then served mainly as a resource person and consultant for the final 12 weeks of the semester. The course was deemed successful, for the students learned mathematical concepts well, developed creative approaches to independent problem solving, and developed an esprit de corps. An expanded version of the course will be taught to large groups in future years. (PB)

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16Introduction To Mathematical Programming: Applications And Algorithms

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A three unit mathematics course entitled Introduction to Computing evaluated the effectiveness of programing as an aid to learning math concepts and to developing student self-reliance. Sixteen students enrolled in the course at the College of Notre Dame in Belmont, California; one terminal was available, connected to the Stanford Computation Center IBM 360/67, and the interactive mode and BASIC were used. Two texts were required--BASIC Manual and Notes for BASIC. Students solved two problems a week in algebra, calculus, or linear algebra for the first eight weeks, providing problem descriptions, flowcharts, program listings, sample outputs, conjectures, and conclusions. In the last half of the course each student completed a major individual project. The teacher lectured on programing concepts and BASIC in the early part of the course and then served mainly as a resource person and consultant for the final 12 weeks of the semester. The course was deemed successful, for the students learned mathematical concepts well, developed creative approaches to independent problem solving, and developed an esprit de corps. An expanded version of the course will be taught to large groups in future years. (PB)

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17Mathematical Programming For Management And Business

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A three unit mathematics course entitled Introduction to Computing evaluated the effectiveness of programing as an aid to learning math concepts and to developing student self-reliance. Sixteen students enrolled in the course at the College of Notre Dame in Belmont, California; one terminal was available, connected to the Stanford Computation Center IBM 360/67, and the interactive mode and BASIC were used. Two texts were required--BASIC Manual and Notes for BASIC. Students solved two problems a week in algebra, calculus, or linear algebra for the first eight weeks, providing problem descriptions, flowcharts, program listings, sample outputs, conjectures, and conclusions. In the last half of the course each student completed a major individual project. The teacher lectured on programing concepts and BASIC in the early part of the course and then served mainly as a resource person and consultant for the final 12 weeks of the semester. The course was deemed successful, for the students learned mathematical concepts well, developed creative approaches to independent problem solving, and developed an esprit de corps. An expanded version of the course will be taught to large groups in future years. (PB)

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18Some Contributions To Mathematical Programming

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Book Source: Digital Library of India Item 2015.194103 dc.contributor.author: Purshotam Lal Jolly dc.date.accessioned: 2015-07-08T03:56:28Z dc.date.available: 2015-07-08T03:56:28Z dc.date.digitalpublicationdate: 2005-08-28 dc.identifier.barcode: 1990010092368 dc.identifier.origpath: /rawdataupload/upload/0092/368 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/194103 dc.description.scannerno: 5 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 190 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: In Public Domain dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Natural Sciences dc.subject.classification: Mathematics dc.subject.classification: Geometry dc.title: Some Contributions To Mathematical Programming

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19Mathematical Foundations Of Programming Semantics : 9th International Conference, New Orleans, LA, USA, April 7-10, 1993 : Proceedings

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Book Source: Digital Library of India Item 2015.194103 dc.contributor.author: Purshotam Lal Jolly dc.date.accessioned: 2015-07-08T03:56:28Z dc.date.available: 2015-07-08T03:56:28Z dc.date.digitalpublicationdate: 2005-08-28 dc.identifier.barcode: 1990010092368 dc.identifier.origpath: /rawdataupload/upload/0092/368 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/194103 dc.description.scannerno: 5 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 190 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: In Public Domain dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Natural Sciences dc.subject.classification: Mathematics dc.subject.classification: Geometry dc.title: Some Contributions To Mathematical Programming

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  • Title: ➤  Mathematical Foundations Of Programming Semantics : 9th International Conference, New Orleans, LA, USA, April 7-10, 1993 : Proceedings
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20Management Science : Mathematical Programming And Network Models

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Book Source: Digital Library of India Item 2015.194103 dc.contributor.author: Purshotam Lal Jolly dc.date.accessioned: 2015-07-08T03:56:28Z dc.date.available: 2015-07-08T03:56:28Z dc.date.digitalpublicationdate: 2005-08-28 dc.identifier.barcode: 1990010092368 dc.identifier.origpath: /rawdataupload/upload/0092/368 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/194103 dc.description.scannerno: 5 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 190 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: In Public Domain dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Natural Sciences dc.subject.classification: Mathematics dc.subject.classification: Geometry dc.title: Some Contributions To Mathematical Programming

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21Introduction To Mathematical Programming

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xiv, 582 pages : 23 cm

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22Linear And Nonlinear Programming : An Introduction To Linear Methods In Mathematical Programming

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xiv, 582 pages : 23 cm

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23GAMS For Solving Mathematical Programming Problems

xiv, 582 pages : 23 cm

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24NASA Technical Reports Server (NTRS) 19710014596: Design Of A Document Retrieval System Using Pattern Recognition And Mathematical Programming Techniques

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Design and testing of document retrieval system based on development of Boolean file searching instructions and pattern recognition

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25Mathematical Programming 1996: Vol 75 Index

Mathematical Programming 1996: Volume 75 , Issue Index. Digitized from IA1653230-03 . Previous issue: sim_mathematical-programming_1996-09-30_74_3_0 . Next issue: sim_mathematical-programming_1996-10-31_75_1_0 .

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26Mathematical Programming 1990: Vol 48 Index

Mathematical Programming 1990: Volume 48 , Issue Index. Digitized from IA1653230-05 . Previous issue: sim_mathematical-programming_1990-08_47_3_0 . Next issue: sim_mathematical-programming_1990-09_48_2_0 .

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27Mathematical Programming 1994: Vol 65 Index

Mathematical Programming 1994: Volume 65 , Issue Index. Digitized from IA1653230-03 . Previous issue: sim_mathematical-programming_1994-05-11_64_3_0 . Next issue: sim_mathematical-programming_1994-05-31_65_1_0 .

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28Mathematical Programming 1995: Vol 71 Index

Mathematical Programming 1995: Volume 71 , Issue Index. Digitized from IA1653230-03 . Previous issue: sim_mathematical-programming_1995-11-20_70_3_0 . Next issue: sim_mathematical-programming_1995-11-30_71_1_0 .

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29Mathematical Programming 1997: Vol 77 Index

Mathematical Programming 1997: Volume 77 , Issue Index. Digitized from IA1652525-04 . Previous issue: sim_mathematical-programming_1997-03-01_76_3 . Next issue: sim_mathematical-programming_1997-04-01_77_1 .

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30Modularity-Maximizing Network Communities Via Mathematical Programming

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In many networks, it is of great interest to identify "communities", unusually densely knit groups of individuals. Such communities often shed light on the function of the networks or underlying properties of the individuals. Recently, Newman suggested "modularity" as a natural measure of the quality of a network partitioning into communities. Since then, various algorithms have been proposed for (approximately) maximizing the modularity of the partitioning determined. In this paper, we introduce the technique of rounding mathematical programs to the problem of modularity maximization, presenting two novel algorithms. More specifically, the algorithms round solutions to linear and vector programs. Importantly, the linear programing algorithm comes with an a posteriori approximation guarantee: by comparing the solution quality to the fractional solution of the linear program, a bound on the available "room for improvement" can be obtained. The vector programming algorithm provides a similar bound for the best partition into two communities. We evaluate both algorithms using experiments on several standard test cases for network partitioning algorithms, and find that they perform comparably or better than past algorithms.

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31Mathematical Programming; An Introduction To The Design And Application Of Optimal Decision Machines. --

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xi, 496 p. : 23 cm. --

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32Mathematical Programming : The State Of The Art, Bonn 1982

xi, 496 p. : 23 cm. --

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33Mathematical Programming And The Analysis Of Capital Budgeting Problems

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xi, 496 p. : 23 cm. --

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34Mathematical Programming And The Aircraft Squadron.

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xi, 496 p. : 23 cm. --

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35Sparsity Constrained Minimization Via Mathematical Programming With Equilibrium Constraints

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Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on Iterative Hard Thresholding (IHT). In this paper, we consider a class of continuous optimization techniques based on Mathematical Programs with Equilibrium Constraints (MPECs) to solve general sparsity constrained problems. Specifically, we reformulate the problem as an equivalent biconvex MPEC, which we can solve using an exact penalty method or an alternating direction method. We elaborate on the merits of both proposed methods and analyze their convergence properties. Finally, we demonstrate the effectiveness and versatility of our methods on several important problems, including feature selection, segmented regression, MRF optimization, trend filtering and impulse noise removal. Extensive experiments show that our MPEC-based methods outperform state-of-the-art techniques, especially those based on IHT.

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36Mathematical Aspects Of Logic Programming Semantics

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Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on Iterative Hard Thresholding (IHT). In this paper, we consider a class of continuous optimization techniques based on Mathematical Programs with Equilibrium Constraints (MPECs) to solve general sparsity constrained problems. Specifically, we reformulate the problem as an equivalent biconvex MPEC, which we can solve using an exact penalty method or an alternating direction method. We elaborate on the merits of both proposed methods and analyze their convergence properties. Finally, we demonstrate the effectiveness and versatility of our methods on several important problems, including feature selection, segmented regression, MRF optimization, trend filtering and impulse noise removal. Extensive experiments show that our MPEC-based methods outperform state-of-the-art techniques, especially those based on IHT.

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37Introduction To Mathematical Programming Applications And Algorithms (for Windows)

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Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on Iterative Hard Thresholding (IHT). In this paper, we consider a class of continuous optimization techniques based on Mathematical Programs with Equilibrium Constraints (MPECs) to solve general sparsity constrained problems. Specifically, we reformulate the problem as an equivalent biconvex MPEC, which we can solve using an exact penalty method or an alternating direction method. We elaborate on the merits of both proposed methods and analyze their convergence properties. Finally, we demonstrate the effectiveness and versatility of our methods on several important problems, including feature selection, segmented regression, MRF optimization, trend filtering and impulse noise removal. Extensive experiments show that our MPEC-based methods outperform state-of-the-art techniques, especially those based on IHT.

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38Mathematical Programming 1988: Vol 42 Index

Mathematical Programming 1988: Volume 42 , Issue Index. Digitized from IA1653230-05 . Previous issue: sim_mathematical-programming_1988-04_40_3_0 . Next issue: sim_mathematical-programming_1988-04_42_1_0 .

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39Mathematical Programming 1990 - 1991: Vol 49 Index

Mathematical Programming 1990 - 1991: Volume 49 , Issue Index. Digitized from IA1652525-04 . Previous issue: sim_mathematical-programming_1986-1989_34-45_cumulative-index . Next issue: sim_mathematical-programming_1990-11_49_1 .

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40Mathematical Programming 1990 - 1991: Vol 49 Index

Mathematical Programming 1990 - 1991: Volume 49 , Issue Index. Digitized from IA1653230-05 . Previous issue: sim_mathematical-programming_1986-1989_34-45_cumulative-index_0 . Next issue: sim_mathematical-programming_1990-11_49_1_0 .

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41Mathematical Programming 1996: Vol 73 Index

Mathematical Programming 1996: Volume 73 , Issue Index. Digitized from IA1652525-04 . Previous issue: sim_mathematical-programming_1996-03-31_72_3 . Next issue: sim_mathematical-programming_1996-04-30_73_1 .

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42Mathematical Programming 1996: Vol 73 Index

Mathematical Programming 1996: Volume 73 , Issue Index. Digitized from IA1653230-03 . Previous issue: sim_mathematical-programming_1996-03-31_72_3_0 . Next issue: sim_mathematical-programming_1996-04-30_73_1_0 .

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43Mathematical Programming 1997: Vol 78 Index

Mathematical Programming 1997: Volume 78 , Issue Index. Digitized from IA1653230-03 . Previous issue: sim_mathematical-programming_1997-06-01_77_3_0 . Next issue: sim_mathematical-programming_1997-07-01_78_1_0 .

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44Mathematical Programming 1997: Vol 79 Table Of Contents

Mathematical Programming 1997: Volume 79 , Issue CONTENTS. Digitized from IA1652525-04 . Previous issue: sim_mathematical-programming_1997_79_index . Next issue: sim_mathematical-programming_1997-10-01_79_1-3 .

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45Mathematical Programming 1997: Vol 79 Index

Mathematical Programming 1997: Volume 79 , Issue Index. Digitized from IA1653230-03 . Previous issue: sim_mathematical-programming_1997-09-01_78_3_0 . Next issue: sim_mathematical-programming_1997_79_contents_0 .

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46Mathematical Foundations Of Programming Language Semantics : 3rd Workshop, Tulane University, New Orleans, Louisiana, USA, April 8-10, 1987 : Proceedings

Mathematical Programming 1997: Volume 79 , Issue Index. Digitized from IA1653230-03 . Previous issue: sim_mathematical-programming_1997-09-01_78_3_0 . Next issue: sim_mathematical-programming_1997_79_contents_0 .

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47Mathematical Programming 1998: Vol 80 Index

Mathematical Programming 1998: Volume 80 , Issue Index. Digitized from IA1652525-04 . Previous issue: sim_mathematical-programming_1997-10-01_79_1-3 . Next issue: sim_mathematical-programming_1998-01-01_80_1 .

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48Computer Assisted Decision Making : Expert Systems, Decision Analysis, Mathematical Programming

By

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49Mathematical Programming 1992: Vol 57 Index

Mathematical Programming 1992: Volume 57 , Issue Index. Digitized from IA1653230-05 . Previous issue: sim_mathematical-programming_1992-10-05_56_3_0 . Next issue: sim_mathematical-programming_1992-05-04_57_1_0 .

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50Mathematical Programming : State Of The Art 1994

Mathematical Programming 1992: Volume 57 , Issue Index. Digitized from IA1653230-05 . Previous issue: sim_mathematical-programming_1992-10-05_56_3_0 . Next issue: sim_mathematical-programming_1992-05-04_57_1_0 .

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