相关论文: Commutation principles for optimization problems i…

The goal of this paper is to address some optimal control and shape optimisation problems arising from bulk-surface cooperative systems. The basic model under consideration is the following: letting $\Omega$ be a fixed domain, we assume…

Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality…

This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits H\"{o}lder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we…

Motivated by Fredholm theory, we develop a framework to establish the convergence of spectral methods for operator equations $\mathcal L u = f$. The framework posits the existence of a left-Fredholm regulator for $\mathcal L$ and the…

This paper proposes a collocation boundary element method based on the Burton--Miller method for solving transmission problems, which is rapidly convergent within the Krylov subspace solver framework. Our study enhances Burton--Miller-type…

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…

We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate…

This paper discusses a generalization of spectral representations related to convex one-homogeneous regularization functionals, e.g. total variation or $\ell^1$-norms. Those functionals serve as a substitute for a Hilbert space structure…

We study the problem of minimizing or maximizing the fundamental spectral gap of Schr\"odinger operators on metric graphs with either a convex potential or a ``single-well'' potential on an appropriate specified subset. (In the case of…

We refine the understanding of continuous dependence on coefficients of solution operators under the nonlocal $H$-topology viz Schur topology in the setting of evolutionary equations in the sense of Picard. We show that certain components…

This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of…

Optimization problems involving the minimization of a finite sum of smooth, possibly non-convex functions arise in numerous applications. To achieve a consensus solution over a network, distributed optimization algorithms, such as…

We introduce a transfer matrix method for the spectral analysis of discrete Hermitian operators with locally finite hopping. Such operators can be associated with a locally finite graph structure and the method works in principle on any…

Whereas in a coordinate-dependent setting the Euler-Lagrange equations establish necessary conditions for solving variational problems in which both the integrands of functionals and the resulting paths are assumed to be sufficiently…

This is a survey on the use of Fourier transformation methods in the treatment of boundary problems for the fractional Laplacian $(-\Delta)^a$ (0<a<1), and pseudodifferential generalizations P, over a bounded open set $\Omega$ in $R^n$. The…

This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…

Semidefinite programming is based on optimization of linear functionals over convex sets defined by linear matrix inequalities, namely, inequalities of the form $$L_A(X)=I-A_1X_1-\dots-A_g X_g\succeq0.$$ Here the $X_j$ are real numbers and…

This work is about the use of regularized optimal-transport distances for convex, histogram-based image segmentation. In the considered framework, fixed exemplar histograms define a prior on the statistical features of the two regions in…

We provide sufficient conditions for quantitative convergence of the iterates of proximal splitting algorithms for minimizing a sum of functions on a metric space. The theory does not assume that the functions have common minima, nor does…

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…