We present here a characterization of the generalized derivative of the optimal value of the objective function of a linear program as a function of matrix coefficients. We generalize the result of Freund (1985) to the cases where derivatives may not be defined because of the existence of multiple primal or dual solutions. Subject classification : Parametric Linear Programming, Linear Programmi...

Optimization problems with complementarity constraints are closely related to optimization problems with variational inequality constraints and bilevel programming problems. In this paper, under mild constraint qualifications, we derive some necessary and sufficient optimality conditions involving the proximal coderivatives. As an illustration of applications, the result is applied to the bilev...

The main ideas of path following by predictor-corrector and piecewise-linear methods, and their application in the direction of homotopy methods and non-linear eigenvalue problems are reviewed. Further new applications to areas such as polynomial systems of equations, linear eigenvalue problems, interior methods for linear programming, parametric programming and complex bifurcation are surveyed...

DEA (Data Envelopment Analysis) is a technique for evaluating the relative effectiveness of decision-making units (DMU) with multiple inputs and outputs data based on non-parametric modeling using mathematical programming (including linear programming, multi-parameter programming, stochastic programming, etc.). The classical DEA methods are developed to handle the information in the form of cri...

In this paper, we propose the use of lexicographic parametric programming to recognize efficient units in Data Envelopment Analysis (DEA). By using the parameterization of the rhs vector of the envelopment problem, we obtain the efficiency curve which is traversing through the efficient frontier from unit to unit. The units in the basis with any parameter value are efficient and the unit domina...

A mathematical programming approach to deal with the global configuration of resource constraints is presented. A specialized parametric programming algorithm to obtain the pareto set for the biobjective problem that appears to deal with the global configuration for 0-1-Integer Linear Programing problems is presented and implemented. Computational results for Multiconstrained Knapsack problems ...