Related papers: 2x2 convexifications for convex quadratic optimiza…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
The aim of this manuscript is to approach by means of first order differential equations/inclusions convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the…
We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…
In this paper it is shown that the compact linearization approach, that has been previously proposed only for binary quadratic problems with assignment constraints, can be generalized to arbitrary linear equations with positive coefficients…
This paper is concerned with optimal power flow (OPF), which is the problem of optimizing the transmission of electricity in power systems. Our main contributions are as follows: (i) we propose a novel parabolic relaxation, which transforms…
We associate with each convex optimization problem, posed on some locally convex space, with infinitely many constraints indexed by the set T, and a given non-empty family H of finite subsets of T, a suitable Lagrangian-Haar dual problem.…
We consider extensions of the Shannon relative entropy, referred to as $f$-divergences.Three classical related computational problems are typically associated with these divergences: (a) estimation from moments, (b) computing normalizing…
The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely…
This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we…
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally NP-hard, we show it is polynomial time solvable when a…
We consider the problem of approximating nonconvex quadratic optimization with ellipsoid constraints (ECQP). We show some SDP-based approximation bounds for special cases of (ECQP) can be improved by trivially applying the extened Pataki's…
This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…
This paper investigates a model-free solution to the stochastic linear quadratic regulation (LQR) problem for linear discrete-time systems with both multiplicative and additive noises. We formulate the stochastic LQR problem as a nonconvex…
A new approach to the local and global explanation is proposed. It is based on selecting a convex hull constructed for the finite number of points around an explained instance. The convex hull allows us to consider a dual representation of…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
We consider the multilinear polytope defined as the convex hull of the feasible region of a linearized binary polynomial optimization problem. We define a relaxation in an extended space for this polytope, which we refer to as the complete…
We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a…