Error bounds, facial residual functions and applications to the exponential cone

Abstract We construct a general framework for deriving error bounds conic feasibility problems. In particular, our approach allows one to work with cones that fail be amenable or even have computable projections, two previously challenging barriers. For the purpose, we first show how may constructed using objects called one-step facial residual functions . Then, develop several tools compute these in absence of closed form expressions projections onto cones. demonstrate use and power results by computing tight exponential cone problem. Interestingly, discover natural example which tightest bound is related Boltzmann–Shannon entropy. were also able produce an sets Hölderian holds but supremum set admissible exponents not itself exponent.