网页Very flat regions. Widely varying curvature. Source: https://commons.wikimedia.org/wiki/File:Saddle_point.svg. But is it actually that hard? Yes, non-convex optimization is at least NP-hard. Can encode most problems as non-convex optimization problems. Example: subset sum problem.
Recent Theoretical Advances in Non-Convex Optimization
网页2020年12月11日 — Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical results on global performance guarantees of optimization algorithms for non-convex optimization.
Modern Nonconvex Nondifferentiable Optimization - SIAM …
网页Serving as an important impetus for this monograph, this chapter introduces a host of nonconvex nondifferentiable optimization problems in several variables that arise from modern statistics-based learning models formulated as an expected-value minimization problem with variable selections.
[1712.07897] Non-convex Optimization for Machine Learning
网页2017年12月21日 — View a PDF of the paper titled Non-convex Optimization for Machine Learning, by Prateek Jain and Purushottam Kar. A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems.
网页Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which …
Topics in Nonconvex Optimization - Springer
网页Nonconvex Optimization is a multi-disciplinary research field that deals with the characterization and computation of local/global minima/maxima of nonlinear, nonconvex, nonsmooth, discrete and continuous functions.
Finite-Time Nonconvex Optimization Using Time-Varying
网页3 天之前 — In this paper, we study the finite-time convergence of the time-varying dynamical systems for solving convex and nonconvex optimization problems in different scenarios. We first show the asymptotic convergence of the trajectories of dynamical systems while only requiring convexity of the objective function. Under the Kurdyka–Łojasiewicz (KL) exponent of the objective function, we establish ...
Recent Theoretical Advances in Non-Convex Optimization
网页2022年4月5日 — Policies and ethics. Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical results on global performance...
非凸优化（Non-convex optimization）领域有什么起到基石作 …
网页第一类是求解全局最优的NP-Hardness的证明。. 很多 形式极其简单 的非凸问题被证明是NP-hard，比如标准二次规划 (StQP)或协正性检验 (等价于 \min\ {x^TDx:x\ge0\} )。. 这些论文打破了我们求解全局最优的幻想。. 第二类是求解平稳解的迭代复杂度。. 求解局部最优解 …
网页Definition 7.1. A first-order critical point of f satisfies. ∇f(x) = 0. If f is convex, any 1st-order critical point is a global minimizer. Finding 1st-order stationary point is sufficient for convex optimization. Example: gradient descent (GD) How about nonconvex optimization?
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