Related papers: Dual gradient method for ill-posed problems using …
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…
In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…
In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy…
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…
We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we…
Many optimization problems require hyperparameters, i.e., parameters that must be pre-specified in advance, such as regularization parameters and parametric regularizers in variational regularization methods for inverse problems, and…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
For objects belonging to a known model set and observed through a prescribed linear process, we aim at determining methods to recover linear quantities of these objects that are optimal from a worst-case perspective. Working in a Hilbert…
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
Learning methods in Banach spaces are often formulated as regularization problems which minimize the sum of a data fidelity term in a Banach norm and a regularization term in another Banach norm. Due to the infinite dimensional nature of…
We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…
In this paper we consider a distributed convex optimization problem over time-varying networks. We propose a dual method that converges R-linearly to the optimal point given that the agents' objective functions are strongly convex and have…
In this paper, we consider the dual formulation of minimizing $\sum_{i\in I}f_i(x_i)+\sum_{j\in J} g_j(\mathcal{A}_jx)$ with the index sets $I$ and $J$ being large. To address the difficulties from the high dimension of the variable $x$…
We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging…
In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…
We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level…
We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized…