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In this paper, we use new approach for linear factorized quadratic optimization and a quadratic fractional optimization problem. We observed that there is change in the rule of selecting entering vector at initial stage and for some quadratic optimization problem; it takes more number of iteration to achieve optimality. Here at the initial step we choose the entering vector on the basis of new rules of method described below. Like a linear fractional programming problem (LFPP), linear factorized quadratic optimization problem (LFQOP) and quadratic fractional optimization problem (LFQFOP) can be usefully applied in a wide range of real-world applications. These are useful in solving the problem in economics whenever the different economic activities utilize the fixed resources in proportion to the level of their values, hospital and health care planning, financial planning etc. In the last few decades a lot of research papers and monographs were published throughout the world where authors investigated different theoretical and algorithmic aspects of QOP and QFO problems in various forms. Quadratic fractional program is an optimization problem wherein one either minimizes or maximizes a quadratic fractional objective function subject to finite number of linear inequality or equality constraints. In this paper, we propose solution methods for linear factorized quadratic optimization problem and factorized quadratic fractional optimization problem with new approach.

Solution Methods for Linear Factorized Quadratic Optimization and Quadratic Fractional Optimization Problem