Related papers: A Note on Cores and Quasi Relative Interiors in Pa…
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…
The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator concavity property leads to numerous concavity and convexity results for other matrix…
This paper discusses semiparametric inference on hypotheses on the cointegration and the attractor spaces for $I(1)$ linear processes with moderately large cross-sectional dimension. The approach is based on empirical canonical correlations…
In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…
We study integration and $L^2$-approximation in the worst-case setting for deterministic linear algorithms based on function evaluations. The underlying function space is a reproducing kernel Hilbert space with a Gaussian kernel of tensor…
Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and…
The first two authors of this paper asserted in Lemma 4 of "New Farkas-type constraint qualifications in convex infinite programming" (DOI: 10.1051/cocv:2007027) that a given reverse convex inequality is consequence of a given convex system…
We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…
The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constraint. A natural question arises, namely, if a physically…
We consider the problem of estimating the locations of a set of points in a k-dimensional euclidean space given a subset of the pairwise distance measurements between the points. We focus on the case when some fraction of these measurements…
We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a…
The chase procedure is a fundamental algorithmic tool in databases that allows us to reason with constraints, such as existential rules, with a plethora of applications. It takes as input a database and a set of constraints, and iteratively…
Constraint Programming (CP) solvers typically tackle optimization problems by repeatedly finding solutions to a problem while placing tighter and tighter bounds on the solution cost. This approach is somewhat naive, especially for…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
We consider box-constrained integer programs with objective $g(Wx) + c^T x$, where $g$ is a "complicated" function with an $m$ dimensional domain. Here we assume we have $n \gg m$ variables and that $W \in \mathbb Z^{m \times n}$ is an…
We discuss a weak constraint qualification for conic linear programs and its applications for a few classes of cones. This constraint qualification is used to give a solution to a problem proposed by Shapiro and Z\v{a}linescu and show that…
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…