Four closely related minimax location problems are considered. Each involves locating a point in the plane to minimize the maximum distance (plus a possible constant) to a given finite set of points. The distance meas...
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Four closely related minimax location problems are considered. Each involves locating a point in the plane to minimize the maximum distance (plus a possible constant) to a given finite set of points. The distance measures considered are the Euclidean and the rectilinear. In each case efficient, finite solution procedures are given. The arguments are geometrical.
The present paper makes a comparison between the shortcomings of two kinds of conditions. In the case of direct distribution this condition turns out to be necessary but unfortunately not sufficient and for indirect d...
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The present paper makes a comparison between the shortcomings of two kinds of conditions. In the case of direct distribution this condition turns out to be necessary but unfortunately not sufficient and for indirect distribution the condition is sufficient but not necessary. The insufficiency in the direct and the absence of necessity in the indirect case, which are caused by eventual nonconvexities of the problem, are explored a bit further. A single example is presented.
Dynamic force identification is presented here as a mathematical programming problem. This approach to the identification problem is particularly powerful if the system equations, constraints, and objective function c...
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Dynamic force identification is presented here as a mathematical programming problem. This approach to the identification problem is particularly powerful if the system equations, constraints, and objective function can be expressed as linear functions of the forces sought. In this case the formulation is one of linearprogramming for which large-scale, effective capabilities are available as standard computer software programs.
A geometrical description of Lemke's algorithm is presented for solving the linear complementarity problem. A study is made of the class of all complementary cones and it is shown that, under a regularity conditio...
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A geometrical description of Lemke's algorithm is presented for solving the linear complementarity problem. A study is made of the class of all complementary cones and it is shown that, under a regularity condition on this class, necessary and sufficient conditions for the success of Lemke's algorithm can be proved. It is also shown that this regularity condition is satisfied by some known classes of complementary cones. A class of matrices for which all principal minors are negative is added to the existing classes of matrices for which the linear complementarity problem can be solved by Lemke's algorithm.
Investigation of the possibility of applying the method of feasible directions to optimization problems with mixed inequality constraints for stochastic systems. The optimization method includes solution of an auxilia...
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Investigation of the possibility of applying the method of feasible directions to optimization problems with mixed inequality constraints for stochastic systems. The optimization method includes solution of an auxiliary linearprogramming problem which determines an optimal direction of motion for obtaining the next approximation. In the algorithm, precautionary steps are taken to prevent zigzag motion. This is done by the so-called AZ-method, which excludes sticking of the computational process and ensures the accuracy of computations.
A method of solution for integer linearprogramming problems is proposed that is a synthesis of the two most common methods, the method of cuts and the method of branches and bounds. The method is primarily intended f...
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A method of solution for integer linearprogramming problems is proposed that is a synthesis of the two most common methods, the method of cuts and the method of branches and bounds. The method is primarily intended for approximate solution (with an estimate of the deviation from the optimum) of applied problems of fairly large size.
An elementary approach is suggested to the solution of a nonlinear stochastic programming problem with probabilistic constraints. A complete set of solutions is obtained that opens the possibility of passing to lexico...
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An elementary approach is suggested to the solution of a nonlinear stochastic programming problem with probabilistic constraints. A complete set of solutions is obtained that opens the possibility of passing to lexicographic optimization. Pertinent to control and planning models in engineering and economics.
It is proposed to improve the existing schemes for proof of the existence of optimum plans for a class of extremal problems, including stochastic programming problems with a ″random plan″ , and to consider construct...
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It is proposed to improve the existing schemes for proof of the existence of optimum plans for a class of extremal problems, including stochastic programming problems with a ″random plan″ , and to consider construction of the optimum plans. The general approach is illustrated by three problems that are mathematical models of control under conditions of incomplete information. Earlier results are extended and improved.
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