A family of nonlinear programming problems: minimize θt, u subject to gt, u ≤ 0 and u ≥ 0 is considered, where t is a scalar parameter changing from 0 to +∞, u an n-dimensional variable vector, θ a continuous real valued mapping defined on the 1 + n-dimensional space and g a continuous mapping from the 1 + n-dimensional space into the m-dimensional space. It is assumed that for each fixed t, θt, · and gjt, · j = 1,..., m have partial derivatives ∂θt, u/∂ui and ∂gjt, u/∂uii = 1,..., n, j = 1,..., m which are continuous with respect to both t and u. Under a moderate constraint qualification, this paper applies the complementary pivoting theory to the computation of a piecewise linear path in the product space of the parameter t and the variable vector u from which we can approximately know how a Kuhn-Tucker's stationary solution to the problem moves as the parameter t changes from 0 to any given nonnegative number.
['Masakazu Kojima']
A Complementary Pivoting Approach to Parametric Nonlinear Programming