Related papers: Frank-Wolfe Splitting via Augmented Lagrangian Met…
First-order methods have been studied for nonlinear constrained optimization within the framework of the augmented Lagrangian method (ALM) or penalty method. We propose an improved inexact ALM (iALM) and conduct a unified analysis for…
This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and constraint functions. The algorithm is constructed by…
This article deals with multiobjective composite optimization problems that consist of simultaneously minimizing several objective functions, each of which is composed of a combination of smooth and non-smooth functions. To tackle these…
We introduce a twice differentiable augmented Lagrangian for nonlinear optimization with general inequality constraints and show that a strict local minimizer of the original problem is an approximate strict local solution of the augmented…
Deep neural networks is today one of the most popular choices in classification, regression and function approximation. However, the training of such deep networks is far from trivial as there are often millions of parameters to tune.…
In this project, we reviewed a paper that deals graph-structured convex optimization (GSCO) problem with the approximate Frank-Wolfe (FW) algorithm. We analyzed and implemented the original algorithm and introduced some extensions based on…
In a recent work (arXiv-DOI: 1804.08072v1) we introduced the Modified Augmented Lagrangian Method (MALM) for the efficient minimization of objective functions with large quadratic penalty terms. From MALM there results an optimality…
We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…
The Frank-Wolfe algorithm achieves a convergence rate of $\mathcal{O}(1/T)$ for smooth convex optimization over compact convex domains, accelerating to $\mathcal{O}(1/T^2)$ when both the objective and the feasible set are strongly convex.…
We consider smooth convex minimization over compact convex sets, i.e., $\min_{x \in C} f(x)$ with the (vanilla) Frank-Wolfe algorithm. Well-known lower bounds establish a worst-case $\Omega(1/t)$ primal-gap barrier in the general smooth…
In this paper, we propose an inexact Augmented Lagrangian Method (ALM) for the optimization of convex and nonsmooth objective functions subject to linear equality constraints and box constraints where errors are due to fixed-point data. To…
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
The Frank-Wolfe method is a popular method in sparse constrained optimization, due to its fast per-iteration complexity. However, the tradeoff is that its worst case global convergence is comparatively slow, and importantly, is…
We introduce a few variants on Frank-Wolfe style algorithms suitable for large scale optimization. We show how to modify the standard Frank-Wolfe algorithm using stochastic gradients, approximate subproblem solutions, and sketched decision…
We tackle robust optimization problems under objective uncertainty in the oracle model, i.e., when the deterministic problem is solved by an oracle. The oracle-based setup is favorable in many situations, e.g., when a compact formulation of…
We study Frank-Wolfe algorithms - standard, pairwise, and away-steps - for efficient optimization of Dominant Set Clustering. We present a unified and computationally efficient framework to employ the different variants of Frank-Wolfe…
Projection-free optimization via different variants of the Frank-Wolfe (FW), a.k.a. Conditional Gradient method has become one of the cornerstones in optimization for machine learning since in many cases the linear minimization oracle is…
Symmetric nonnegative matrix factorization has found abundant applications in various domains by providing a symmetric low-rank decomposition of nonnegative matrices. In this paper we propose a Frank-Wolfe (FW) solver to optimize the…
The complexity in large-scale optimization can lie in both handling the objective function and handling the constraint set. In this respect, stochastic Frank-Wolfe algorithms occupy a unique position as they alleviate both computational…
The Conditional Gradient (or Frank-Wolfe) method is one of the most well-known methods for solving constrained optimization problems appearing in various machine learning tasks. The simplicity of iteration and applicability to many…