相关论文: Faster Discrete Convex Function Minimization with …
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
Quasar convexity is a condition that allows some first-order methods to efficiently minimize a function even when the optimization landscape is non-convex. Previous works develop near-optimal accelerated algorithms for minimizing this class…
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…
The expansion in automation of increasingly fast applications and low-power edge devices poses a particular challenge for optimization based control algorithms, like model predictive control. Our proposed machine-learning supported approach…
We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the…
This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…
We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…
Using an optimization algorithm to solve a machine learning problem is one of mainstreams in the field of science. In this work, we demonstrate a comprehensive comparison of some state-of-the-art first-order optimization algorithms for…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
In this paper, we use composite optimization algorithms to solve sigmoid networks. We equivalently transfer the sigmoid networks to a convex composite optimization and propose the composite optimization algorithms based on the linearized…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
In this paper, we consider the minimization of a nonsmooth nonconvex objective function $f(x)$ over a closed convex subset $\mathcal{X}$ of $\mathbb{R}^n$, with additional nonsmooth nonconvex constraints $c(x) = 0$. We develop a unified…
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
Despite the recent development in machine learning, most learning systems are still under the concept of "black box", where the performance cannot be understood and derived. With the rise of safety and privacy concerns in public, designing…