相关论文: A New Algorithm for Linear Programming

This paper presents algorithms for solving multiobjective integer programming problems. The algorithm uses Barvinok's rational functions of the polytope that defines the feasible region and provides as output the entire set of nondominated…

It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…

In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.

In this paper, a robust sequential quadratic programming method for constrained optimization is generalized to problem with an {expectation} objective function {and} deterministic equality and inequality constraints. A stochastic line…

This paper is concerned with linear algebra based methods for solving exactly polynomial systems through so-called Gr\"obner bases, which allow one to compute modulo the polynomial ideal generated by the input equations. This is a topical…

We present an algorithm for marginalising changepoints in time-series models that assume a fixed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables…

In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a…

We propose a novel randomized linear programming algorithm for approximating the optimal policy of the discounted Markov decision problem. By leveraging the value-policy duality and binary-tree data structures, the algorithm adaptively…

Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…

We propose a simple O([n^5/\log n]L) algorithm for linear programming feasibility, that can be considered as a polynomial-time implementation of the relaxation method. Our work draws from Chubanov's "Divide-and-Conquer" algorithm [4], where…

Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…

We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…

We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…

This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler…

In the first part of this work, we develop a novel scheme for solving nonparametric regression problems. That is the approximation of possibly low regular and noised functions from the knowledge of their approximate values given at some…

In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…

We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…