What is the role of convexity in optimization problems?

The Extreme Value Theorem guarantees both a maximum and minimum value for a function under certain conditions. May 20, 2008 ... Abstract. We introduce a resonance method to produce large values of the Riemann zeta-function on the critical line, and large and small central ... Values of related functions Suppose f is differentiable on (-∞,∞) and assume it has a local extreme value at the point x = 2, where f(2) = 0. Extreme Value Theorem If f is continuous on a closed interval [a, b], then f attains both an absolute maximum value M and an absolute minimum. Well within the localization regime, the wave-function intensity distribution is shown to develop a sequence of pre-power-law, power-law, exponential, and ... Then, for a proper choice of the function σ, the limit is (excluding a degenerate distribution) the survival function of a so-called generalized Pareto ... Mar 19, 2014 ... The purpose of this study was to examine and compare two extreme value distribution functions (the Gumbel and the Weibull functions) in modelling the ... Aug 29, 2007 ... We introduce a "resonance" method to produce large values of |\zeta(1/2+it)| and large and small central values of L-functions. ... extreme-value approach with modelling of the galaxy luminosity function. We obtain predictions of the brightest galaxies for a suite of luminosity functions ... ... extreme value statistics remains valid. The proportionality function for the tails can be estimated non-parametrically along with the (common) extreme value ...