The gradient path of a real valued differentiable function is given by the solution of a system of differential equations. For a quadratic function the above equations are linear, resulting in a closed form solution. ...
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The gradient path of a real valued differentiable function is given by the solution of a system of differential equations. For a quadratic function the above equations are linear, resulting in a closed form solution. A quasi-Newton type algorithm for minimizing ann-dimensional differentiable function is presented. Each stage of the algorithm consists of a search along an arc corresponding to some local quadratic approximation of the function being minimized. The algorithm uses a matrix approximating the Hessian in order to represent the arc. This matrix is updated each stage and is stored in its Cholesky product form. This simplifies the representation of the arc and the updating process. Quadratic termination properties of the algorithm are discussed as well as its global convergence for a general continuously differentiable function. Numerical experiments indicating the efficiency of the algorithm are presented.
A new relaxation type two-level method for solving state space constrained dynamic optimization problems is suggested. The method is closely related to the hierarchical approach and on the other hand it can be viewed ...
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A new relaxation type two-level method for solving state space constrained dynamic optimization problems is suggested. The method is closely related to the hierarchical approach and on the other hand it can be viewed as an application of the Hestenes-Powell method of multipliers. The state space constrained original problem is transformed into a control constrained first level problem by using the multiplier method. As in the hierarchical approach the first level problem is dependent on certain Lagrange multiplier type parameters which are determined at the second level. A coordination type iteration process between the two levels results in the solution of the original state constrained, optimization problem. The convergence properties of the method are studied via numerical experiments; analytical convergence results are not available so far.
A computer code, FEASBL, is developed to maximize a non-linear objective function over a convex feasible region. The feasible region is defined by a set of non-linear and linear constraints on the variables. FEASBL ca...
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A computer code, FEASBL, is developed to maximize a non-linear objective function over a convex feasible region. The feasible region is defined by a set of non-linear and linear constraints on the variables. FEASBL can solve prob- lems involving up to fifty variables with a feasible region formed by up to fifty non-linear constraints, and fifty linear constraints. FEASBL uses a feasible direction method as its solution algorithm.
The problem of allocating munitions from M weapons systems to N target complexes is studied and a review of pertinent literature is presented. An algorithm for the solution of the problem in the special case of two we...
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The problem of allocating munitions from M weapons systems to N target complexes is studied and a review of pertinent literature is presented. An algorithm for the solution of the problem in the special case of two weapons systems against N targets is developed and programmed for computerized solution. The results of an example problem are shown and tested. Discussion of the algorithm's extension to more than two weapons systems is included as are alternative solution techniques.
Bakalárska práca je zamerané na nájdenie a popísanie matematického modelu, ktorý rekonštruuje skutočné súčasné finančné náklady na zber a zvoz odpadu na ...
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Bakalárska práca je zamerané na nájdenie a popísanie matematického modelu, ktorý rekonštruuje skutočné súčasné finančné náklady na zber a zvoz odpadu na úrovní obcí s rozšírenou pôsobnosťou, ktoré nie sú ináč dostupné a sú potrebné na ďalšie plánovanie s využiteľným odpadom. Na vytvorenie modelu sú použité znalosti z optimalizácie, štatistiky a teórie grafov, ktoré sú v texte zhrnuté. Model je aplikovaný na skutočné dáta v prostredí GAMS. Výsledky aplikácie sú okomentované a analyzované. Na základe tejto analýzy sú uvedené aj možnosti vývoja tohto modelu.
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