In this paper, we consider the (additive integrality) gap of the cutting stock problem (CSP) and the skiving stock problem (SSP). Formally, the gap is defined as the difference between the optimal values of the ILP and its LP relaxation. For both, the CSP and the SSP, this gap is known to be bounded by … Read more
A common approach to solve stochastic optimization problems with expectations is to replace the expectations by its sample averages. Large sample asymptotic properties of this approximation are well studied when the sample is i.i.d. In many cases, however, i.i.d. samples are not readily available. On the contrary, one can generate a Harris recurrent Markov chain … Read more
This paper develops algorithms for decentralized machine learning over a network, where data are distributed, computation is localized, and communication is restricted between neighbors. A line of recent research in this area focuses on improving both computation and communication complexities. The methods SSDA and MSDA \cite{scaman2017optimal} have optimal communication complexity when the objective is smooth … Read more
A natural and important generalization of submodularity—$k$-submodularity—applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In this paper, we study maximization problems with $k$-submodular objective functions. We propose valid linear inequalities, namely the $k$-submodular inequalities, for the hypograph of any $k$-submodular … Read more
In the application of machine learning to real life decision-making systems, e.g., credit scoring and criminal justice, the prediction outcomes might discriminate against people with sensitive attributes, leading to unfairness. The commonly used strategy in fair machine learning is to include fairness as a constraint or a penalization term in the minimization of the prediction … Read more
This paper establishes the iteration-complexity of an inner accelerated inexact proximal augmented Lagrangian (IAPIAL) method for solving linearly constrained smooth nonconvex composite optimization problems which is based on the classical Lagrangian function and, most importantly, performs a full Lagrangian multiplier update, i.e., no shrinking factor is incorporated on it. More specifically, each IAPIAL iteration consists … Read more
Inverse optimization – determining parameters of an optimization problem that render a given solution optimal – has received increasing attention in recent years. While significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision-making. In this paper, … Read more
We modify the total-variation-regularized image segmentation model proposed by Chan, Esedoglu and Nikolova [SIAM Journal on Applied Mathematics 66, 2006] by introducing local regularization that takes into account spatial image information. We propose some techniques for defining local regularization parameters, based on the cartoon-texture decomposition of the given image, on the mean and median filters, … Read more
In this paper we introduce RAPOSa, a global optimization solver specifically designed for (continuous) polynomial programming problems with box-constrained variables. Written entirely in C++, RAPOSa is based on the Reformulation-Linearization Technique developed by Sherali and Tuncbilek (1992) and subsequently improved in Sherali et al. (2012a), Sherali et al. (2012b) and Dalkiran and Sherali (2013). We … Read more
Equilibrium models for energy markets under uncertain demand and supply have attracted considerable attentions. This paper focuses on modelling crude oil market share under the COVID-19 pandemic using two-stage stochastic equilibrium. We describe the uncertainties in the demand and supply by random variables and provide two types of production decisions (here-and-now and wait-and-see). The here-and-now … Read more