Related papers: Compact extended formulations for low-rank functio…

In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of…

In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the $l_{0}$-norm of a given matrix with a non-convex fraction function on…

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…

We say that a subset of C^n is hypoconvex if its complement is the union of complex hyperplanes. Let D be the closed unit disk in C, T the unit circle. We prove two conjectures of Helton and Marshall. (See ``Frequency domain design and…

In the article the necessary and sufficient conditions for a representation of Lipschitz function of more than two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome…

This work develops a class of relaxations in between the big-M and convex hull formulations of disjunctions, drawing advantages from both. The proposed "P-split" formulations split convex additively separable constraints into P partitions…

Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…

We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradients must satisfy to ensure the existence of a global…

This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. Most of the existing methods assume the extent to which the given tasks are related or share a…

Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…

We address the issue of generating cutting planes for mixed integer programs from multiple rows of the simplex tableau with the tools of disjunctive programming. A cut from q rows of the simplex tableau is an intersection cuts from a…

We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…

This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) incompatible…

This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…

Using polarity, we give an outer polyhedral approximation for the epigraph of set functions. For a submodular function, we prove that the corresponding polar relaxation is exact; hence, it is equivalent to the Lov\'asz extension. The polar…

We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…

We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a…

In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function on a uniform grid. Both the problem of estimating the support function at a point and that of estimating…

Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…