Related papers: A compact representation for minimizers of $k$-sub…
The problem of maximizing nonnegative monotone submodular functions under a certain constraint has been intensively studied in the last decade, and a wide range of efficient approximation algorithms have been developed for this problem.…
Submodularity is an important concept in integer and combinatorial optimization. A classical submodular set function models the utility of selecting homogenous items from a single ground set, and such selections can be represented by binary…
In submodular $k$-partition, the input is a non-negative submodular function $f$ defined over a finite ground set $V$ (given by an evaluation oracle) along with a positive integer $k$ and the goal is to find a partition of the ground set…
Under mild assumptions, we prove that any random multifunction can be represented as the set of minimizers of an infinitely many differentiable normal integrand, which preserves the convexity of the random multifunction. We provide several…
Let p be an arbitrary prime number and k be an algebraically closed field of characteristic l different from p. We construct maximal simple k-types of Levi subgroups M' of SLn(F), when F is a non-archimedean locally compact field of…
We consider the problem of minimizing a polynomial function over the integer lattice. Though impossible in general, we use a known sufficient condition for the existence of continuous minimizers to guarantee the existence of integer…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
We develop a framework for the distributed minimization of submodular functions. Submodular functions are a discrete analog of convex functions and are extensively used in large-scale combinatorial optimization problems. While there has…
We consider the problem of minimizing the composition of a nonsmooth function with a smooth mapping in the case where the proximity operator of the nonsmooth function can be explicitly computed. We first show that this proximity operator…
In minimization models for image recovery and data analysis problems, loss functions and linear operators are typically aggregated as an average of composite terms. Each term in the aggregate models a desired property of the ideal solution…
Motivated by recent advances in solution methods for mixed-integer convex optimization (MICP), we study the fundamental and open question of which sets can be represented exactly as feasible regions of MICP problems. We establish several…
This paper proposes a Heaviside composite optimization approach and presents a progressive (mixed) integer programming (PIP) method for solving multi-class classification and multi-action treatment problems with constraints. A Heaviside…
We formulate the issue of minimality of self-adjoint operators on a Hilbert space as a semi-definite problem, linking the work by Overton in [1] to the characterization of minimal hermitian matrices. This motivates us to investigate the…
Let G be a compact p-adic analytic group. We study K-theoretic questions related to the representation theory of the completed group algebra kG of G with coefficients in a finite field k of characteristic p. We show that if M is a finitely…
In discrete optimization, representing an objective function as an $s$-$t$ cut function of a network is a basic technique to design an efficient minimization algorithm. A network representable function can be minimized by computing a…
Submodular optimization has numerous applications such as crowdsourcing and viral marketing. In this paper, we study the fundamental problem of non-negative submodular function maximization subject to a $k$-system constraint, which…
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is…
Unconstrained binary integer programming (UBIP) is a challenging optimization problem due to the presence of binary variables. To address the challenge, we introduce a novel class of functions named sharp-peak functions (SPFs), which…
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it…