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We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the…
Inverse optimization is the problem of determining the values of missing input parameters for an associated forward problem that are closest to given estimates and that will make a given target vector optimal. This study is concerned with…
Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method…
In this paper we propose an extension of the iteratively regularized Gauss--Newton method to the Banach space setting by defining the iterates via convex optimization problems. We consider some a posteriori stopping rules to terminate the…
This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…
We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary…
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…
This paper presents a novel approach to construct regularizing operators for severely ill-posed Fredholm integral equations of the first kind by introducing parametrized discretization. The optimal values of discretization and…
Building on the well-known total-variation (TV), this paper develops a general regularization technique based on nonlinear isotropic diffusion (NID) for inverse problems with piecewise smooth solutions. The novelty of our approach is to be…
In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…
In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite…
This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for…
Tikhonov regularization is one of the most commonly used methods of regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to…
We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters…
We consider multi-agent, convex optimization programs subject to separable constraints, where the constraint function of each agent involves only its local decision vector, while the decision vectors of all agents are coupled via a common…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…