Demonstration of the main capabilities of the Performance Estimation Methodology. Exact worst-case analysis of a fixed-step first-order method on \(L\)-smooth convex functions. Edit the method; the performance estimation problem is solved again in your browser.
\(\displaystyle x_i \;=\; x_0 - \frac{1}{L}\sum_{j} H_{ij}\,\nabla f(x_j), \qquad i = 1,\dots,N\)
In a number box, type a value, drag up or down with the mouse, or use the arrow keys.
Multiplier \(\lambda_{ij}\) (row \(i\), column \(j\)) weights the interpolation inequality \(Q_{ij} = f_i - f_j - \langle g_j,\, x_i - x_j\rangle - \tfrac{1}{2L}\|g_i - g_j\|^2 \ge 0\), with \(f_i = f(x_i)\), \(g_i = \nabla f(x_i)\) and \(*\) the minimizer.