Related papers: Zero-One Laws for Random Feasibility Problems
We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. This defines a stochastic linear program for which, under general conditions, we characterize the fluctuations…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
We study large random matrices with i.i.d. entries conditioned to have prescribed row and column sums (margins), a problem connected to relative entropy minimization, Schr\"odinger bridges, contingency tables, and random graphs with given…
A formal link between regression and classification has been tenuous. Even though the margin maximization term $\|w\|$ is used in support vector regression, it has at best been justified as a regularizer. We show that a regression problem…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
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 study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
The uniform quadratic optimizatin problem (UQ) is a nonconvex quadratic constrained quadratic programming (QCQP) sharing the same Hessian matrix. Based on the second-order cone programming (SOCP) relaxation, we establish a new sufficient…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
Ensuring fairness in computational problems has emerged as a $key$ topic during recent years, buoyed by considerations for equitable resource distributions and social justice. It $is$ possible to incorporate fairness in computational…
We introduce the $(p,q)$-Fair Clustering problem. In this problem, we are given a set of points $P$ and a collection of different weight functions $W$. We would like to find a clustering which minimizes the $\ell_q$-norm of the vector over…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
For random combinatorial optimization problems, there has been much progress in establishing laws of large numbers and computing limiting constants for the optimal value of various problems. However, there has not been as much success in…
Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…
We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of…
Robust optimization is concerned with constructing solutions that remain feasible also when a limited number of resources is removed from the solution. Most studies of robust combinatorial optimization to date made the assumption that every…
In this paper, we consider the problem of finding an almost surely common fixed point of a family of paracontraction maps indexed on a probability space, which we refer to as the stochastic feasibility problem. We show that a random…
In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…