The minimum cut and maximum flow problems form a well-known pair of dual problems providing a min-max relation. Similarly, the continuous relaxation of the minimum multicut problem is the linear dual ...

A revision of an earlier DI using three-discrete solution interface a PWM to switching regulator and a method to decrease settling time.

We formulate this problem as a nonlinear Generalized Disjunctive Program (GDP), which, following transformation, results in a large-scale mixed-integer nonlinear programming (MINLP) problem. This ...

Loopwise route representation (LRR), which has been recently proposed as an alternative network representation, can determine the optimal path for the vehicle routing problems with a simpler ...

OpenAI on Friday unveiled a new artificial intelligence system, OpenAI o3, which is designed to “reason” through problems involving math, science and computer programming.

OpenAI claims that o1-preview outperforms its predecessor, GPT-4o, on multiple benchmarks, including competitive programming, mathematics, and "scientific reasoning." ...

They solve industrial-scale problems all the time,” sometimes with tens of thousands of variables, he said. Integer [Linear] Programming Algorithms for integer programming often take a first stab at a ...

We assume that the k -linear factors of the upper level problem and the l -linear factors of the lower level problem to be non-negative. In this paper, we propose an algorithm based on branch-and-cut ...