A polytope $P\subseteq [0,1]^n$ is said to have the \emph{persistency} property if for every vector $c\in \R^{n}$ and every $c$-optimal point $x\in P$, there exists a $c$-optimal integer point $y\in P\cap \{0,1\}^n$ such that $x_i = y_i$ for each $i \in \{1,\dots,n\}$ with $x_i \in \{0,1\}$. In this paper, we consider a relaxation of the … Read more
This paper considers monotone transformations of the objective space of multiobjective optimization problems which leave the set of efficient points invariant. Under mild assumptions, for the standard ordering cone we show that such transformations must be component-wise transformations. The same class of transformations also leaves the sets of weakly and of Geoffrion properly efficient points … Read more
Adaptive update schemes for penalty parameters are crucial to enhancing robustness and practical applicability of penalty methods for constrained optimization. However, in the context of general constrained stochastic optimization, additional challenges arise due to the randomness introduced by adaptive penalty parameters. To address these challenges, we propose an Adaptive Single-loop Stochastic Penalty method (AdaSSP) in … Read more
This tutorial provides an overview of the current state-of-the-art in the sensitivity analysis for nonlinear programming. Building upon the fundamental work of Fiacco, it derives the sensitivity of primal-dual solutions for regular nonlinear programs and explores the extent to which Fiacco’s framework can be extended to degenerate nonlinear programs with non-unique dual solutions. The survey … Read more
Maintenance strategies are pivotal in ensuring the reliability and performance of critical components within industrial machines and systems. However, accurately determining the optimal replacement time for such components under stress and deterioration remains a complex task due to inherent uncertainties and variability in operating conditions. In this paper, we propose a comprehensive approach based on … Read more
The proximal bundle method (PBM) is a fundamental and computationally effective algorithm for solving nonsmooth optimization problems. In this paper, we present the first variant of the PBM for smooth objectives, achieving an accelerated convergence rate of \(\frac{1}{\sqrt{\epsilon}}\log(\frac{1}{\epsilon})\), where \(\epsilon\) is the desired accuracy. Our approach addresses an open question regarding the convergence guarantee of … Read more
The Chance-Constrained Parallel Machine Scheduling Problem (CC-PMSP) assigns jobs with uncertain processing times to machines, ensuring that each machine’s availability constraints are met with a certain probability. We present a decomposition approach where the master problem assigns jobs to machines, and the subproblems schedule the jobs on each machine while verifying the solution’s feasibility under … Read more
With food waste levels of about 30%, mostly caused by overproduction, reducing food waste poses an important challenge in the food service sector. As food is prepared in advance rather than on demand, there is a significant risk that meals or meal components remain uneaten. Flexible meal planning can promote the reuse of these leftovers … Read more
Gas transportation and storage has become one of the most relevant and important optimization problems in energy systems. This problem inherently includes highly nonlinear and nonconvex aspects due to gas physics, and discrete aspects due to the control decisions of active network elements. Obtaining even locally optimal solutions for this problem presents significant mathematical and … Read more
In the continuous time service network design problem, a freight carrier decides the path of shipments in their network as well as the dispatch times of the vehicles transporting the shipments. State-of-the-art algorithms to solve this problem are based on the dynamic discretization discovery framework. These algorithms solve a relaxation of the problem using a … Read more