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Dual Problem (dual + problem)

Distribution by Scientific Domains

Engineering	22%
Business, Economics, Finance and Accounting	22%

Selected Abstracts

Strategies for computing goal-oriented a posteriori error measures in non-linear elasticity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2002
Fredrik Larsson
Abstract We investigate the characteristics and performance of goal-oriented a posteriori error measures for a class of non-linear elasticity models, while restriction is made to small strain theory. The chosen error measure of the displacement field can be global or local (probing the chosen quantity in a specific spatial point). The error is computable with the aid of the solution of a dual problem whose data depend on the error measure. The main thrust of the paper is to evaluate the performance of a few different approximation strategies for computing the dual solution. The chosen strategies are compared in terms of accuracy, ease of implementation, reliability and cost-efficiency. A well-known numerical example, the Cook's membrane, is used for the numerical evaluations. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A dual extremum principle in thermodynamics ,

AICHE JOURNAL, Issue 8 2007
Alexander Mitsos
Abstract Phase equilibria of multicomponent mixtures are considered and a reinterpretation of the Gibbs tangent plane stability criterion is proposed via Lagrangian duality. The starting point is the natural primal problem of minimizing the Gibbs free energy subject to material balance. The stable phase split is the solution of the corresponding dual problem, providing a necessary and sufficient dual extremum principle. Only in the absence of duality gap is the physical phase split also the solution of the primal problem. The only requirements are continuity of the Gibbs free energy and the trivial requirement that each species is present in the overall composition. The number of phases is permitted to be infinite, and does not need to be known a priori. No assumption is made on the presence of all species in all phases. Case studies are presented based on the NRTL and UNIQUAC activity coefficient model. © 2007 American Institute of Chemical Engineers AIChE J, 2007 [source]

DUALITY IN OPTIMAL INVESTMENT AND CONSUMPTION PROBLEMS WITH MARKET FRICTIONS

MATHEMATICAL FINANCE, Issue 2 2007
I. Klein
In the style of Rogers (2001), we give a unified method for finding the dual problem in a given model by stating the problem as an unconstrained Lagrangian problem. In a theoretical part we prove our main theorem, Theorem 3.1, which shows that under a number of conditions the value of the dual and primal problems is equal. The theoretical setting is sufficiently general to be applied to a large number of examples including models with transaction costs, such as Cvitanic and Karatzas (1996) (which could not be covered by the setting in Rogers [2001]). To apply the general result one has to verify the assumptions of Theorem 3.1 for each concrete example. We show how the method applies for two examples, first Cuoco and Liu (1992) and second Cvitanic and Karatzas (1996). [source]

Simultaneous solution of Lagrangean dual problems interleaved with preprocessing for the weight constrained shortest path problem

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2009
Ranga Muhandiramge
Abstract Conventional Lagrangean preprocessing for the network Weight Constrained Shortest Path Problem (WCSPP), for example Beasley and Christofides (Beasley and Christofides, Networks 19 (1989), 379,394), calculates lower bounds on the cost of using each node and edge in a feasible path using a single optimal Lagrange multiplier for the relaxation of the WCSPP. These lower bounds are used in conjunction with an upper bound to eliminate nodes and edges. However, for each node and edge, a Lagrangean dual problem exists whose solution may differ from the relaxation of the full problem. Thus, using one Lagrange multiplier does not offer the best possible network reduction. Furthermore, eliminating nodes and edges from the network may change the Lagrangean dual solutions in the remaining reduced network, warranting an iterative solution and reduction procedure. We develop a method for solving the related Lagrangean dual problems for each edge simultaneously which is iterated with eliminating nodes and edges. We demonstrate the effectiveness of our method computationally: we test it against several others and show that it both reduces solve time and the number of intractable problems encountered. We use a modified version of Carlyle and Wood's (38th Annual ORSNZ Conference, Hamilton, New Zealand, November, 2003) enumeration algorithm in the gap closing stage. We also make improvements to this algorithm and test them computationally. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009 [source]

Diabetes care in Brazil: now and in the future

PRACTICAL DIABETES INTERNATIONAL (INCORPORATING CARDIABETES), Issue 2 2004
HC Pedrosa MD Professor of Medicine
Abstract Brazil, like many other developing countries, faces the dual problem of an increasing burden of chronic disease together with many communicable diseases. The organisation of diabetes care and the provision of drugs have improved considerably over the last 20 years, and the Brazilian Diabetes Society has had a major role in these improvements. However, many people remain unaware that they have diabetes and some diagnosed patients receive no treatment. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Galerkin-type space-time finite elements for volumetrically coupled problems

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Holger Steeb Dipl.-Ing.
The study focuses on error estimation techniques for a coupled problem with two constituents based on the Theory of Porous Media. After developing space-time finite elements for this mixed problem, we extend the numerical scheme to a coupled space-time adaptive strategy. Therefore, an adjoint or dual problem is formulated and discussed, which is solved lateron numerically. One advantage of the presented technique is the high flexibility of the error indicator with respect to the error measure. [source]

Lagrange Multipliers as Marginal Rates of Substitution in Multi-Constraint Optimization Problems

METROECONOMICA, Issue 1 2001
Christian E. Weber
This paper shows that, when a function is optimized subject to several binding constraints, some of the Lagrange multipliers in the dual problems can be interpreted as marginal rates of substitution among certain arguments in the generalized indirect objective function for the primal problem. It also shows how to calculate these Lagrange multipliers from observable price,quantity data. Three particular examples are discussed: a firm that minimizes costs subject to both fixed output and rationing constraints, a household that maximizes utility subject to both income and time constraints, and portfolio choice under uncertainty treated as a multiple constraint optimization problem. [source]