Abstract: The convex conjugate of a function is a fundamental dual construction in convex optimization. This talk will discuss a novel convex conjugate approach to analyze some of the most popular first-order algorithms for convex minimization. We will highlight how the convex conjugate approach gives a unified and succinct derivation of the convergence rates of the subgradient, gradient, and accelerated gradient algorithms. We will also show that the convex conjugate approach readily extends to more general Bregman proximal methods. The talk will be accessible to anyone with a basic background on multivariate calculus. Bio: Javier Peña is the Bajaj Family Professor of Operations Research at the Tepper School of Business, Carnegie Mellon University. Prior to joining Carnegie Mellon, he earned his PhD in Applied Mathematics from Cornell University and held a postdoctoral position at the Mathematical Sciences Research Institute in Berkeley, California. He does research on theory and algorithms for convex optimization, applications of optimization models in finance and machine learning, and equilibrium computation in game theory.