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We propose a stronger formulation of the precedence constraints and the station limits for the simple assembly line balancing problem. The linear relaxation of the improved integer program theoretically dominates all previous formulations…
Patriksson (2008) provided a then up-to-date survey on the continuous,separable, differentiable and convex resource allocation problem with a single resource constraint. Since the publication of that paper the interest in the problem has…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
We present a model predictive control (MPC) framework to solve the constrained nonlinear output regulation problem. The main feature of the proposed framework is that the application does not require the solution to classical regulator…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using Neural…
Coded distributed computing (CDC) was introduced to greatly reduce the communication load for MapReduce computing systems. Such a system has $K$ nodes, $N$ input files, and $Q$ Reduce functions. Each input file is mapped by $r$ nodes and…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. The computational complexity of VCSPs depends on the set of allowed cost functions in the input. Recently, the computational…
The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as…
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…
While approaches to model the progression of fracture have received significant attention, methods to find the solution to the associated nonlinear equations have not. In general, nonlinear solution methods and optimization methods have a…
We consider the problem of finding (possibly non connected) discrete surfaces spanning a finite set of discrete boundary curves in the three-dimensional space and minimizing (globally) a discrete energy involving mean curvature. Although we…
In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed…
We discuss technical results on learning function approximations using piecewise-linear basis functions, and analyze their stability and convergence using nonlinear contraction theory.
The strengthening of linear relaxations and bounds of mixed integer linear programs has been an active research topic for decades. Enumeration-based methods for integer programming like linear programming-based branch-and-bound exploit…
We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is still able to fully describe rotation of…