c-optimal designs for weighted polynomial models

c-optimal design problems for weighted polynomial models are discussed. Vectors c, where c-optimal designs are supported by some extreme points of a certain equioscillating function, are characterized, and this equioscillating function is a linear combination of the regression functions. These results are then applied to the no-intercept model in which the optimal designs for estimating certain individual parameters can be found. Examples of applications of the above results in finding locally c-optimal designs for some nonlinear models are discussed. Finally the results are extended to a more general linear model.