Related papers: Combinatorial Algorithm for Tropical Linearly Fact…
The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…
In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…
Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require…
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
The predict+optimize problem combines machine learning ofproblem coefficients with a combinatorial optimization prob-lem that uses the predicted coefficients. While this problemcan be solved in two separate stages, it is better to…
We consider decision problems of rating alternatives based on their pairwise comparisons according to two criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall scores of the alternatives. We…
The tropical arithmetic operations on $\mathbb{R}$ are defined by $a\oplus b=\min\{a,b\}$ and $a\otimes b=a+b$. Let $A$ be a tropical matrix and $k$ a positive integer, the problem of Tropical Matrix Factorization (TMF) asks whether there…
This paper presents a first-order distributed algorithm for solving a convex semi-infinite program (SIP) over a time-varying network. In this setting, the objective function associated with the optimization problem is a summation of a set…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to…
Tropical geometry is a degeneration of classical geometry which loose the property of unique factorization for polynomials. In this paper we explore a structure that is known to be a semi-degeneration between the classical algebra and the…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
We present a new, unifying approach following some recent developments on the complexity of neural networks with piecewise linear activations. We treat neural network layers with piecewise linear activations as tropical polynomials, which…
We study the projected gradient descent method on low-rank matrix problems with a strongly convex objective. We use the Burer-Monteiro factorization approach to implicitly enforce low-rankness; such factorization introduces non-convexity in…
The Fr\'{e}chet mean is a fundamental notion of central tendency defined as a minimizer of a sum of squared distances in a general metric space. In this paper, we study Fr\'{e}chet means in tropical geometry -- a piecewise linear,…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
Let ${\mathcal D}^{k,l}(m,n)$ be the set of all the integer points in the transportation polytope of $kn\times ln$ matrices with row sums $lm$ and column sums $km$. In this paper we find the sharp lower bound on the tropical determinant…
In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial…
An algorithm is designed which decomposes a tropical univariate rational function into a composition of tropical binomials and trinomials. When a function is monotone, the composition consists just of binomials. Similar algorithms are…