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We present a procedure to numerically compute finite step worst caseperformance guarantees on a given algorithm for the unconstrained optimizationof strongly convex functions with Lipschitz continuous gradients. The solutionmethod provided serves as an alternative approach to that derived by Taylor,Hendrickx, and Glineur in [Math. Prog. 161 (1-2), 2017]. The difference lies inthe fact that our solution uses conditions for the interpolation of a set ofpoints and gradient evaluations by the gradient of a function in the class ofinterest, whereas their solution uses conditions for the interpolation of a setof points, gradient evaluations, and function evaluations by a function in theclass of interest. The motivation for this alternative solution is that, inmany cases, neither the algorithm nor the performance metric of interest relyupon function evaluations. The primary development is a procedure to avoidsuffering from the factorial growth in the number of these conditions with thesize of the set to be interpolated when solving for the worst case performance.

Finite Step Performance of First-order Methods Using Interpolation Conditions Without Function Evaluations