On the convergence of con- ditional epsilon-subgradient methods for convex programs and convex-concave saddle-point problems. European Journal of Operational Research, 151(3):461- 473, 2003.Larsson, T., Patriksson, M., Stro¨mberg, A.B.: On the convergence of conditional ε-subgradient ...
In this section, we focus on analyzing the performance of optimistic gradient descent ascent (OGDA) for solving a general smooth convex-concave saddle point problem. It has been shown that the OGDA method recovers the convergence rate of the proximal point for both strongly convex-strongly concav...
Proximal Point Approximations Achieving a Convergence Rate of O(1/k)O(1/k) for Smooth Convex-Concave Saddle Point Problems: Optimistic Gradient and Extra-gradient Methods (2019) On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems (2019) The algorithm by Ferson et al. is surprisingly...
Ouyang, Y., Xu, Y.: Lower complexity bounds of first-order methods for convex–concave bilinear saddle-point problems. Math. Program.185, 1–35 (2021) MathSciNetGoogle Scholar Zhang, J., Hong, M., Zhang, S.: On lower iteration complexity bounds for the convex concave saddle point probl...
composite CP problems are in a sense “conceptual” since they require the minimization of the summation of a prox-function together with the composition of\(\varPsi \)with an affine transformation [38]. More recently, Nesterov [40] studied a class of nonsmooth convex-concave saddle point ...
它是concave 的,因为 LL 是关于 αα 的线性函数,且 pointwise infimum 保持了 concavity 同时注意到对任意 αα,F(α)≤infx∈Xf(x)=p∗F(α)≤infx∈Xf(x)=p∗ 定义对偶问题Def. Dual problem 为带约束优化问题定义对偶问题,为maxαF(α)subject to:α≥0maxαF(α)subject to:α≥0对偶问题...
This thesis investigates the theoretically properties of commonly used optimization methods on the saddle point problem of the form min θ∈Rn max φ∈Rm f (θ,φ), where f is neither convex in θ nor concave in φ. We show that gradientbased optimization schemes have undesired stable stationa...
optimization problem, requiring the computation of certain ‘error’ functions that, in turn, depend on the solution of a non-concave/non-convex optimizatio... MI Idiart,PP Castañeda - 《Proceedings of the Royal Society A Mathematical Physical & Engineering Sciences》 被引量: 19发表: 2007年...
{111} planes. The <112> directions can be used to form a parallelogrammic structure. The intersection of {111} planes forms either a concave corners (<180 i.e. corners turning inside) or a convex corners (>180° i.e. corners turning outside). Although both types of corners are ...
Bredies, K., Sun, H.: Preconditioned Douglas–Rachford splitting methods for convex-concave saddle-point problems. SIAM J. Numer. Anal. 53(1), 421–444 (2015) Article MathSciNet MATH Google Scholar Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with ...