We investigate the problem of online convex optimization with unknown delays, in which feedback a decision arrives an arbitrary delay. Previous studies have presented delayed gradient descent (DOGD), and achieved regret bound $$O(\sqrt{D})$$ by only utilizing convexity condition, where $$D\ge T$$ is sum delays over T rounds. In this paper, we further exploit strong to improve bound. Specificall...

Consider a bounded strongly pseudo-convex domain Ω with smooth boundary in Cn. Let T be the Toeplitz algebra on Bergman space La2(Ω). That is, is C⁎-algebra generated by operators {Tf:f∈L∞(Ω)}. Extending work [27], [28] special case of unit ball, we show that any such Ω, and {Tf:f∈VObdd}+K are essential commutants each other, where K collection compact On general considered this paper, proofs r...

В данной статье предлагаются методы оптимизации высокого порядка (тензорные методы) для решения двух типов седловых задач. Первый тип — это классическая мин-макс-постановка поиска седловой точки функционала. Второй поиск стационарной функционала задачи путем минимизации нормы градиента этого Очевидно, что стационарная точка не всегда совпадает с точкой оптимума функции. Однако необходимость в р...

The goal of this paper is to study the effect of inexact first-order information on the first-order methods designed for smooth strongly convex optimization problems. It can be seen as a generalization to the strongly convex case of our previous paper [1]. We introduce the notion of (!,L,μ)-oracle, that can be seen as an extension of the (!,L)-oracle (previously introduced in [1]), taking into ...

Abstract We propose some algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. With the key observation of the velocity observable and controllable in the motion, the algorithms simulate the Newton Second Law without friction based on symplectic Euler scheme. From the intuitive analysis of analytical sol...

in this paper, an optimization problem with a linear objective function subject to a consistent finite system of fuzzy relation inequalities using the max-product composition is studied. since its feasible domain is non-convex, traditional linear programming methods cannot be applied to solve it. we study this problem and capture some special characteristics of its feasible domain and optimal s...

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

This paper considers a wide spectrum of regularized stochastic optimization problems where both the loss function and regularizer can be non-smooth. We develop a novel algorithm based on the regularized dual averaging (RDA) method, that can simultaneously achieve the optimal convergence rates for both convex and strongly convex loss. In particular, for strongly convex loss, it achieves the opti...