Related papers: Around a Farkas type Lemma
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…
In view of the minimization of a function which is the sum of a differentiable function $f$ and a convex function $g$ we introduce descent methods which can be viewed as produced by inexact auxiliary problem principleor inexact variable…
This note serves two purposes. Firstly, we construct a counterexample to show that the statement on the convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex optimization problems in a…
Reducing the amount of human supervision is a key problem in machine learning and a natural approach is that of exploiting the relations (structure) among different tasks. This is the idea at the core of multi-task learning. In this context…
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 present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and…
We develop a reverse entropy power inequality for convex measures, which may be seen as an affine-geometric inverse of the entropy power inequality of Shannon and Stam. The specialization of this inequality to log-concave measures may be…
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…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
In this paper, we establish sufficient conditions for the existence of error bounds at infinity for lower semicontinuous inequality systems. We also show that the existence of an error bound at infinity of constraint systems plays an…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…
The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions…
We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point…
A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…
Farkas' lemma for semidefinite programming characterizes semidefinite feasibility of linear matrix pencils in terms of an alternative spectrahedron. In the well-studied special case of linear programming, a theorem by Gleeson and Ryan…
We study the error of the number of points of a unimodular lattice that fall in a strictly convex and analytic set having the origin and that is dilated by a factor $t$. The aim is to generalize the result of a previous article. We first…
We study the finite convergence of iterative methods for solving convex feasibility problems. Our key assumptions are that the interior of the solution set is nonempty and that certain overrelaxation parameters converge to zero, but with a…
Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…
Minkowski's 2nd theorem in the Geometry of Numbers provides optimal upper and lower bounds for the volume of a $o$-symmetric convex body in terms of its successive minima. In this paper we study extensions of this theorem from two different…