Related papers: A Framework for Generalized Benders' Decomposition…
We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…
We propose a hybrid reinforcement and self-supervised learning framework for accelerating generalized Benders decomposition (GBD). In this framework, a graph based reinforcement learning agent operates on a bipartite representation of the…
The necessary decarbonization efforts in energy sectors entail the integration of flexibility assets, as well as increased levels of uncertainty for the planning and operation of power systems. To cope with this in a cost-effective manner,…
A mathematical framework for modelling constrained mixed-variable optimization problems is presented in a blackbox optimization context. The framework introduces a new notation and allows solution strategies. The notation framework allows…
Bi-Level Optimization (BLO) is originated from the area of economic game theory and then introduced into the optimization community. BLO is able to handle problems with a hierarchical structure, involving two levels of optimization tasks,…
We consider a class of a nested optimization problems involving inner and outer objectives. We observe that by taking into explicit account the optimization dynamics for the inner objective it is possible to derive a general framework that…
Benders decomposition with adaptive oracles was proposed to solve large-scale optimisation problems with a column bounded block-diagonal structure, where subproblems differ on the right-hand side and cost coefficients. Adaptive Benders…
Multiobjective combinatorial optimization deals with problems considering more than one viewpoint or scenario. The problem of aggregating multiple criteria to obtain a globalizing objective function is of special interest when the number of…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
We develop a generalized inverse optimization framework for fitting the cost vector of a single linear optimization problem given multiple observed decisions. This setting is motivated by ensemble learning, where building consensus from…
An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior,…
In this paper, we propose a general framework that extends the theory of permutation patterns to higher dimensions and unifies several combinatorial objects studied in the literature. Our approach involves introducing the concept of a…
The distribution network restoration problem is by nature a mixed integer and non-linear optimization problem due to the switching decisions and Optimal Power Flow (OPF) constraints, respectively. The link between these two parts involves…
We propose an enhancement to Benders decomposition (BD) that generates valid inequalities for the convex hull of the Benders reformulation, addressing the limitation that classical BD cuts are typically tight only for the continuous…
The growth in online shopping and third party logistics has caused a revival of interest in finding optimal solutions to the large scale in-transit freight consolidation problem. Given the shipment date, size, origin, destination, and due…
Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum,…
Large language models have demonstrated remarkable capabilities across many tasks, yet face significant challenges when dealing with recursive reasoning problems, those requiring the resolution of nested hierarchical structures. While prior…
In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling…