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This paper presents bounds for the variation of the spectral radius $\lambda(G)$ of a graph $G$ after some perturbations or local vertex/edge modifications of $G$. The perturbations considered here are the connection of a new vertex with,…

This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…

Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…

We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse eigenvalue problem for specific finite…

The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…

In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and…

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…

Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range perturbation of a Jacobi or CMV operator from a finite gap isospectral torus. The special case of eventually periodic operators…

In this paper, we for the first time prove local solvability and stability of an inverse spectral problem for higher-order ($n > 3$) differential operators with distribution coefficients. The inverse problem consists in the recovery of…

We study the spectral behavior of higher order elliptic operators upon domain perturbation. We prove general spectral stability results for Dirichlet, Neumann and intermediate boundary conditions. Moreover, we consider the case of the…

For a purely imaginary sign-definite perturbation of a self-adjoint operator, we obtain exponential representations for the perturbation determinant in both upper and lower half-planes and derive respective trace formulas.

We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…

This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…

Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…

We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…

The adaptive perturbation chooses a non-standard decomposition. The Hamiltonian becomes a sum of solvable and perturbation parts. We calculate the spectrum using the adaptive perturbation method at the leading-order to compare to numerical…

Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…

This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…