4 results
Search Results
2. Locally Lipschitz vector optimization with inequality and equality constraints.
- Author
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Ginchev, Ivan, Guerraggio, Angelo, and Rocca, Matteo
- Subjects
- *
MATHEMATICAL optimization , *MATHEMATICAL analysis , *SIMULATION methods & models , *MATHEMATICS , *LIPSCHITZ spaces - Abstract
The present paper studies the following constrained vector optimization problem: $$\mathop {\min }\limits_C f(x),g(x) \in - K,h(x) = 0$$, where f: ℝ n → ℝ m, g: ℝ n → ℝ p are locally Lipschitz functions, h: ℝ n → ℝ q is C1 function, and C ⊂ ℝ m and K ⊂ ℝ p are closed convex cones. Two types of solutions are important for the consideration, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point x0 to be a w-minimizer and first-order sufficient conditions for x0 to be an i-minimizer are obtained. Their effectiveness is illustrated on an example. A comparison with some known results is done. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
3. Proofs and refutations in the undergraduate mathematics classroom.
- Author
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Larsen, Sean and Zandieh, Michelle
- Subjects
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MATHEMATICS , *MATHEMATICAL ability , *MATHEMATICAL linguistics , *MATHEMATICS education , *MATHEMATICAL analysis , *INSTRUCTIONAL systems , *MATHEMATICAL instruments , *MATHEMATICAL variables , *MATHEMATICAL optimization - Abstract
In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional approaches that support the learning of mathematics through the process of guided reinvention. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
4. Dimensioning and on-line scheduling in Lambda Grids using divisible load concepts.
- Author
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Thysebaert, Pieter, Volckaert, Bruno, Leenheer, Marc, Turck, Filip, Dhoedt, Bart, and Demeester, Piet
- Subjects
- *
LAMBDA calculus , *MATHEMATICAL logic , *MATHEMATICAL optimization , *MATHEMATICAL analysis , *MATHEMATICS , *GRID computing , *COMPUTER systems , *DISTRIBUTED computing , *HIGH performance computing , *ELECTRONIC data processing , *SUPERCOMPUTERS - Abstract
Due to the large amounts of data required to be processed by the typical Grid job, it is conceivable that the use of optical transport networks in Grid deployment (hence the term “Lambda Grid”) will increase. The exact topology of the interconnecting network is obtained by solving a dimensioning problem, and the outcome of this strongly depends on both the expected workload characteristics and Grid scheduling policy. Solving this combined scheduling and dimensioning problem using straightforward ILP modelling is cumbersome; however, for steady-state Grid operation, Divisible Load Theory (DLT) can yield scalable formulations of this problem. In this paper, the on-line hierarchical scheduling on a lambda Grid of workload approaching the Grid’s capacity in a two-tier Grid mode of operation is studied. A number of these algorithms are goal-driven, in the sense that target per-resource goals are obtained from the off-line solution to the Divisible Load model. We compare these on-line multiresource scheduling policies for different workloads, Grid interconnection topologies and Grid parameters. We show that these algorithms perform well in the studied scenarios when compared to a fully centralized scheduling algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
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