The use of piecewise polynomial interpolation to generate best L1 approximates

For a locally convex space E and f :E→R¯, we introduce and study surrogate conjugate functionals of f, which en¬compass the quasi-conjugates 1] , pseudo-conjugates 2] and semi-conjugates 3] of f. Also, we introduce and study surro¬gate convexity of sets GcE and of functionals f:E→R¯ and show their connections with surrogate conjugation and with W-conve-xity of sets 4] and of functionals 5], where WcR¯^E. We outline some further developments (surrogate conjugates at a point, surrogate subdifferentials) and an application to optimization. A basic role is played by the concept of a universally defined multifunction A:RXE^*→2^E