tucker conditions

In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent to fractional objective functions. Then on using the Kuhn-Tucker optimality condition of the lower level problem, we transform the linear bilevel programming problem into a corresponding single level programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty, that can be reduce to a single objective function. In the other words, suitable transformations can be applied to formulate FBLP problems. Finally a numerical example is given to illustrate the complexity of the procedure to the solution.

This paper presents a Taylor series approach for solving linear fractional de- centralized bi-level multi-objective decision-making (LFDBL-MODM) problems with a single decision maker at the upper level and multiple decision makers at the lower level. In the proposed approach, the membership functions associated with each objective(s) of the level(s) of LFDBL-MODM are transformed by using a Taylor series and then they are unified. On using the Kuhn-Tucker conditions, the problem is finally reduced to a single objective. Numerical example is given in order to illustrate the efficiency and superiority of the proposed approach.

This work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations AX=B and XC=D with orthogonal constraint. By optimal correction approach, a general representation of the orthogonal solution is obtained. This method is tested on two examples to show that the optimal correction is eective and highly accurate.