How much patience do you have? A worst-case perspective on smooth nonconvex optimization
نویسندگان
چکیده
" 'Though you be swift as the wind, I will beat you in a race' , said the tortoise to the hare. " (Aesop)
منابع مشابه
On the Oracle Complexity of First-Order and Derivative-Free Algorithms for Smooth Nonconvex Minimization
The (optimal) function/gradient evaluations worst-case complexity analysis available for the Adaptive Regularizations algorithms with Cubics (ARC) for nonconvex smooth unconstrained optimization is extended to finite-difference versions of this algorithm, yielding complexity bounds for first-order and derivative free methods applied on the same problem class. A comparison with the results obtai...
متن کاملA note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function
This short note considers and resolves the apparent contradiction between known worst-case complexity results for first and second-order methods for solving unconstrained smooth nonconvex optimization problems and a recent note by Jarre (2011) implying a very large lower bound on the number of iterations required to reach the solution’s neighbourhood for a specific problem with variable dimension.
متن کاملOn the Evaluation Complexity of Composite Function Minimization with Applications to Nonconvex Nonlinear Programming
We estimate the worst-case complexity of minimizing an unconstrained, nonconvex composite objective with a structured nonsmooth term by means of some first-order methods. We find that it is unaffected by the nonsmoothness of the objective in that a first-order trust-region or quadratic regularization method applied to it takes at most O(ǫ−2) function-evaluations to reduce the size of a first-or...
متن کاملمدیر موفق کیست؟
Who is a really successful manager? A manager who spends less money, or the one who earns more? A manager who can survive for a longer period of time, or an administrator who expands his organization, and opens up new branches? Which one is the most successful? The article tries to answer these questions and provides, some simple guidlines for the managers in every domain of management who wan...
متن کاملA trust region algorithm with a worst-case iteration complexity of O(ϵ -3/2) for nonconvex optimization
We propose a trust region algorithm for solving nonconvex smooth optimization problems that, in the worst case, is able to drive the norm of the gradient of the objective function below a prescribed threshold of > 0 after at most O( −3/2) iterations, function evaluations, and derivative evaluations. This improves upon the O( −2) bound known to hold for some other trust region algorithms and mat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012