Certain shortcomings are described in the second order converse duality results in the recent work of (J. Zhang and B. Mond, Bull. Austral. Math. Soc. 55(1997) 29-44). Appropriate modifications are suggested.
Certain shortcomings are described in the second order converse duality results in the recent work of (J. Zhang and B. Mond, Bull. Austral. Math. Soc. 55(1997) 29-44). Appropriate modifications are suggested.
We consider a linear programming problem with unknown objective function. Random observations related to the unknown objective function are sequentially available. We define a stochastic algorithm, based on the simple...
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We consider a linear programming problem with unknown objective function. Random observations related to the unknown objective function are sequentially available. We define a stochastic algorithm, based on the simplex method, that estimates an optimal solution of the linear programming problem. It is shown that this algorithm converges with probability one to the set of optimal solutions and that its failure probability is of order inversely proportional to the sample size. We also introduce stopping criteria for the algorithm. The asymptotic normality of some suitably defined residuals is also analyzed. The proposed estimation algorithm is motivated by the stochastic approximation algorithms but it introduces a generalization of these techniques when the linear programming problem has several optimal solutions. The proposed algorithm is also close to the stochastic quasi-gradient procedures, though their usual assumptions are weakened.
This paper proposes an interactive fuzzy programming method for seeking a satisfactory solution for multiobjective two-level linear fractional programming problems in which the decision makers in the upper and lower l...
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This paper proposes an interactive fuzzy programming method for seeking a satisfactory solution for multiobjective two-level linear fractional programming problems in which the decision makers in the upper and lower levels have several objectives, by first setting up the fuzzy goals for several objectives of each decision maker and seeking a satisfactory solution for the degree of satisfaction of two decision makers in a cooperative manner. In the proposed method, the decision maker at the upper level sets the minimal satisfactory levels for each fuzzy goal and the decision maker at the lower level determines the aspiration levels. The minimal satisfactory levels are treated as a constraint and the solution closest to the aspiration levels of the decision maker at the lower level is computed. The ratio of the aggregative degrees of satisfaction of the decision makers in the upper and lower levels with the obtained solution is evaluated by using partial information on the preference of the decision makers. If the ratio of the degrees of satisfaction satisfies the given condition and the decision maker at the upper level is satisfied with this solution, then the interaction is complete. Otherwise, a satisfactory solution is sought by updating the minimal satisfactory and aspiration levels. (C) 2003 Wiley Periodicals, Inc.
We examine to what extent one can provide characterizations of the sets of solutions to quasiconvex programs using adapted subdifferentials which generalize known characterizations in the convex case.
We examine to what extent one can provide characterizations of the sets of solutions to quasiconvex programs using adapted subdifferentials which generalize known characterizations in the convex case.
This paper explores the consequences for the l(1)-optimal controller of the dual linear programming problem having multiple solutions, for linear time-invariant single-input/single-output systems. When the dual proble...
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This paper explores the consequences for the l(1)-optimal controller of the dual linear programming problem having multiple solutions, for linear time-invariant single-input/single-output systems. When the dual problem has multiple solutions, all solutions yield the same set of optimal controllers. If these multiple solutions comprise an entire face of the constraint region, there is a single optimal controller. Thus, if the constraint region is two-dimensional, the primal and dual problems cannot both have multiple solutions. An example is given with a three-dimensional constraint region where both problems have multiple solutions.
In this paper, we deal with actual problems on production and work force assignment in a housing material manufacturer and a subcontract firm. We formulate two kinds of two-level programming problems;one is a profit m...
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In this paper, we deal with actual problems on production and work force assignment in a housing material manufacturer and a subcontract firm. We formulate two kinds of two-level programming problems;one is a profit maximization problem of both the housing material manufacturer and the subcontract firm, and the other is a profitability maximization problem of them. Applying the interactive fuzzy programming for two-level linear and linear fractional programming problems, we derive satisfactory solutions to the problems. After comparing the two problems, we discuss the results of the applications and examine actual planning of the production and the work force assignment of the two firms to be implemented. (C) 2001 Elsevier Science B.V. All rights reserved.
An approach toward kinetic mechanism reduction both in terms of reactions and species, is discussed. The driving force of the approach is to derive reduced kinetic models while maintaining the structural integrity of ...
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An approach toward kinetic mechanism reduction both in terms of reactions and species, is discussed. The driving force of the approach is to derive reduced kinetic models while maintaining the structural integrity of the detailed mechanisms. The mechanism reduction problem is defined as an integer optimization problem with binary variables denoting the existence/nonexistence of reactions or species. A Branch & Bound framework is implemented for the solution of the resulting mathematical programming problem. Several examples, utilizing a variety of kinetic networks, are presented and the results are analyzed.
In this paper, we present a generalization of the Hessian matrix toC1,1 functions, i.e., to functions whose gradient mapping is locally Lipschitz. This type of function arises quite naturally in nonlinear analysis and...
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In this paper, we present a generalization of the Hessian matrix toC1,1 functions, i.e., to functions whose gradient mapping is locally Lipschitz. This type of function arises quite naturally in nonlinear analysis and optimization. First the properties of the generalized Hessian matrix are investigated and then some calculus rules are given. In particular, a second-order Taylor expansion of aC1,1 function is derived. This allows us to get second-order optimality conditions for nonlinearly constrained mathematical programming problems withC1,1 data.
A problem is considered of the allocation of resources so as to maximize the minimum return from several activities. Optimality conditions are given for the case of a single resource, and are used to derive a solution...
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A problem is considered of the allocation of resources so as to maximize the minimum return from several activities. Optimality conditions are given for the case of a single resource, and are used to derive a solution algorithm. problems with several resources cannot be solved by resourcewise optimization. Concave return functions are treated approximately by linear programming, and optimality or almost optimality of any feasible solution to such a problem can be evaluated by the solution of a linear programming problem. The evaluation measure is extended to certain feasible solutions of problems which have continuous, but not necessarily concave, return functions. A numerical example is given.
Necessary and sufficient conditions for a linear programming problem whose parameters (both in constraints and in the objective function) are prescribed by intervals are given under which any linear programming proble...
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Necessary and sufficient conditions for a linear programming problem whose parameters (both in constraints and in the objective function) are prescribed by intervals are given under which any linear programming problem with parameters being fixed in these intervals has a finite optimum.
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