A fast algorithm for a class of generalized fractional programs

Article Abstract:

There are many decision problems of fractural structure where the criteria are expressed as ratios such as return on investment, liquidity and productivity. Some applications of fractional types of programming can be found in the von Neumann model of economic growth, rational Chebyshev approximation and eigenvalue problems. A new algorithm for the numerical solution of these problems is introduced that differs from the algorithms presented by Crouzeix and Ferland (1991). Unlike the Crouzeix and Ferland solutions, the new algorithm guarantees superlinear speed of convergence. It involves computing a solution and a corresponding dual solution of a convex auxiliary problem in each step, but the sequence of these solutions does not have to be convergent.

Analysis, Convergence (Mathematics)

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An algorithm for a class of nonconvex programming problems with nonlinear fractional objectives

Article Abstract:

When modeling decision systems appropriate for either public policy making or capital investment planning, the model maker encounters fractional criterion functions. In such situations the algorithm developed here would be helpful, since it identifies a desirable set of target values for given nonconvex programming problems. The primary and secondary equations for the algorithm developed are provided and explained. The basic concept behind the algorithmic maximization solution is the minimization of penalties occurring when fractional objectives deviate from target values.

Research, Models, Case studies, Capital investments, Nonlinear programming

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Connectedness in Multiple Linear Fractional Rrogramming

Article Abstract:

Efficient and weakly efficient solutions of multiple linear fractional programming problems are studied. Attention is focused on the geometric properties of sets of these solutions. Weakly efficient solutions are path-connected.

Linear programming, Sets, Mathematics of Computing, Scientific Research, Programming, Mathematical Programming

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