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The Big Data phenomenon has spawned large-scale linear programming problems. In many cases, these problems are non-stationary. In this paper, we describe a new scalable algorithm called NSLP for solving high-dimensional, non-stationary…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…
Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…
Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of…
A novel robust nonlinear model predictive control strategy is proposed for systems with nonlinear dynamics and convex state and control constraints. Using a sequential convex approximation approach and a difference of convex functions…
Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
The augmentation scheme provides a nontraditional approach to nonlinear integer programming by iteratively refining incumbent solutions along objective-improving directions from the Graver basis. Its main computational bottleneck, however,…
Sequence segmentation is a well-studied problem, where given a sequence of elements, an integer K, and some measure of homogeneity, the task is to split the sequence into K contiguous segments that are maximally homogeneous. A classic…
In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
This paper presents a novel outer approximation algorithm for nonsmooth mixed-integer nonlinear programming (MINLP) problems. The method proceeds by fixing the integer variables and solving the resulting nonlinear convex subproblem. When…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…