Some applications of Bombieri's estimate for exponential sums
Wenpeng Zhang, Yuan Yi (2003)
Acta Arithmetica
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Displaying similar documents to “Asymptotic convergence of the steepest descent method for the exponential penalty in linear programming.”
Some applications of Bombieri's estimate for exponential sums
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A method for solving large convex optimization problems is presented. Such problems usually contain a big linear part and only a small or medium nonlinear part. The parts are tackled using two specialized (and thus efficient) external solvers: purely nonlinear and large-scale linear with a quadratic goal function. The decomposition uses an alteration of projection methods. The construction of the method is based on the zigzagging phenomenon and yields a non-asymptotic convergence, not...
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Asymptotic and exponential decay in mean square for delay geometric Brownian motion
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We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions are written in terms of the parameters and are explicit for the case of asymptotic decay. For exponential decay, they are easily resolvable numerically. The analytical method is based on construction of a Lyapunov functional (asymptotic decay) and a forward-backward estimate for the square mean (exponential decay). ...