approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformu-lation of the problem of interest and solving the resulting problem by a fast First Order saddle point method utilizing smoothness of the saddle point cost function....
We consider the convex-concave saddle point problem $\min_{x}\max_{y} f(x)+y^op A x-g(y)$ where $f$ is smooth and convex and $g$ is smooth and strongly convex. We prove that if the coupling matrix $A$ has full column rank, the vanilla primal-dual gradient method can achieve...
We develop new parameter-free and scale-free algorithms for solving convex-concave saddle-point problems. Our results are based on a new simple regret minimizer, the Conic Blackwell Algorithm+ (CBA+), which attains O(1/T) average regret. Intuitively, our approach generalizes to other decision ...
Structured Prediction via the Extragradient Method. We formulate the estimation problem as a convex-concave saddle-point problem and apply the extragradient method, yielding an algorithm with linear convergence... B Lacoste - DBLP 被引量: 59发表: 2006年 加载更多来源...
In this paper we propose three $p$-th order tensor methods for $\mu$-strongly-convex-strongly-concave saddle point problems (SPP). The first method is based on the assumption of $p$-th order smoothness of the objective and it achieves a convergence rate of $O \left( \left( \frac{L...
Last Iterate is Slower than Averaged Iterate in Smooth Convex-Concave Saddle Point Problems (2020) Consensus-Based Optimization on the Sphere I: Well-Posedness and Mean-Field Limit (2020) Consensus-based Optimization on the Sphere II: Convergence to Global Minimizers and Machine Learning (2020) St...
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...
2024A BSTRACTWe revisit the smooth convex-concave bilinearly-coupled saddle-point problem of the formmin x max y f(x) + ⟨y,Bx⟩ − g(y) . In the highly specif ic case where each of the functions f(x) andg(y) is either aff ine or strongly convex, there exist lower bounds...
On Well-Structured Convex-Concave Saddle Point Problems and Variational Inequalities with Monotone Operators For those acquainted with CVX (aka disciplined convex programming) of M. Grant and S. Boyd, the motivation of this work is the desire to extend the scope of CVX beyond convex minimization ...
Mirror Descent Algorithms with Nearly Dimension-Independent Rates for Differentially-Private Stochastic Saddle-Point Problems We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the polyhedral setting. We propose $(\\varepsilon, \\delta... T González,C Gu...