Related papers: An Optimization Approach to Parameter Identificati…
The paper is concerned with a class of nonlinear free boundary problems, which are usually solved by variational methods based on primal (or primal-dual) variational settings. We deduce and investigate special relations (error identities).…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
Inverse optimization seeks to recover unknown objective parameters from observed decisions, yet fundamental questions about when recovery is possible have received limited formal treatment. This paper develops a comprehensive theoretical…
We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies…
We propose techniques for approximating bilevel optimization problems with non-smooth lower level problems that can have a non-unique solution. To this end, we substitute the expression of a minimizer of the lower level minimization problem…
We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters…
We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce…
We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics…
In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…
This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is…
We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…