We consider a nonlinear minimax allocation problem with multiple knapsack-type resource constraints. Each term in the objective function is a nonlinear, strictly decreasing and continuous function of a single variable...
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We consider a nonlinear minimax allocation problem with multiple knapsack-type resource constraints. Each term in the objective function is a nonlinear, strictly decreasing and continuous function of a single variable. All variables are continuous and nonnegative. A previous algorithm for such problem repeatedly solves relaxed problems without the nonnegativity constraints. That algorithm is particularly efficient for certain nonlinear functions for which there are closed-form solutions for the relaxed problems;for other functions, however, the algorithm must employ search methods. We present a new algorithm that uses at each iteration simple-to-compute algebriac expressions to check optimality conditions, instead of solving the relaxed minimax problems. The new algorithm is therefore significantly more efficient for more general nonlinear functions.
This paper presents a new algorithm for globally minimizing a separable, concave function over a compact convex set. The algorithm uses partial outer approximation and branch and bound. The major computational effort ...
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This paper presents a new algorithm for globally minimizing a separable, concave function over a compact convex set. The algorithm uses partial outer approximation and branch and bound. The major computational effort required is solving linear programming problems at some nodes of the branch and bound tree, and solving simple univariate minimizations in some iterations. The algorithm partially mitigates the rapid growth in the number of constraints of the linear programs that would frequently occur if traditional outer approximation were used. Furthermore, unlike outer approximation, the algorithm does not explicitly construct polyhedra which contain the feasible region.
Two nonlinear algorithms for processing vector-valued signals are introduced. The algorithms, called vector median operations, are derived from two multidimensional probability density functions using the maximum-like...
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Two nonlinear algorithms for processing vector-valued signals are introduced. The algorithms, called vector median operations, are derived from two multidimensional probability density functions using the maximum-likelihood-estimate approach. The underlying probability densities are exponential, and the resulting operations have properties very similar to those of the median filter. In the vector median approach, the samples of the vector-valued input signal are processed as vectors. The operation inherently utilizes the correlation between the signal components, giving the filters some desirable properties. General properties as well as the root signals of the vector median filters are studied. The vector median operation is combined with linear filtering, resulting in filters with improved noise attenuation and filters with very good edge response. An efficient algorithm for implementing long vector median filters is presented. The noise attenuation of the filters is discussed, and an application to velocity filtering is shown
We formulate and solve a dual version of the Continuous Collapsing Knapsack Problem using a geometric approach. Optimality conditions are found and an algorithm is presented. Computational experience shows that this p...
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We formulate and solve a dual version of the Continuous Collapsing Knapsack Problem using a geometric approach. Optimality conditions are found and an algorithm is presented. Computational experience shows that this procedure is efficient.
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