Phi Hoang TRAN

Phi Hoang TRAN

PhD student in Applied Mathematics

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portfolio

publications

Solving Nonlinear Absolute Value Equations

Published in arXiv preprint, 2026

This paper studies nonlinear absolute value equations.

Recommended citation: Daniilidis, A., Haddou, M., Le, T. M., Ley, O., & Tran, P. H. (2024). Solving Nonlinear Absolute Value Equations. arXiv preprint arXiv:2402.16439.
Download Paper

scientific_events

SEAMS School 2026 on Applying Mathematics to Real-World Problems

Published:

The aim is to understand the practical uses of mathematics and specifically to solve problems in industry. The course design is focused on concrete industrial problems and incorporates distinct branches of mathematics, covering modeling, theoretical, numerical, computational and simulation aspects. As a consequence we hope to stimulate groups to start researching in specific industry areas, and in general to motivate young mathematicians to work on real-world mathematical problems.

Recent Developments in Analysis and PDEs

Published:

The aim is to understand the practical uses of mathematics and specifically to solve problems in industry. The course design is focused on concrete industrial problems and incorporates distinct branches of mathematics, covering modeling, theoretical, numerical, computational and simulation aspects. As a consequence we hope to stimulate groups to start researching in specific industry areas, and in general to motivate young mathematicians to work on real-world mathematical problems.

talks

Solving Nonlinear Absolute Value Equations

Published:

Abstract. In this work, we show that several problems naturally represented as Nonlinear Absolute Value Equations (NAVE) can be reformulated as Nonlinear Complementarity Problems (NCP) and efficiently solved using smoothing regularization techniques under mild assumptions. As far as we know, this is the first numerical approach that directly deals with NAVE. We also identify a technical assumption commonly utilized in smoothing techniques and prove its equivalence to a classical Łojasiewicz inequality at infinity, validating its non-restrictive nature. Furthermore, we extend established error estimates for NCP solvers to derive error bounds for NAVE problems under weaker assumptions. We illustrate the effectiveness of our approach through applications including asymmetric ridge optimization and nonlinear ordinary differential equations.

Mutualisation de tournées entre marchands à Rungis

Published:

Abstract. In this topic, we will focus on vehicle routing problems. Let’s begin by describing the problem Califrais faces daily: a non-shared vehicle routing problem. The rungismarket.com platform allows its customers to place orders the day before to receive their products the following day. Therefore, it is only at midnight on the day of delivery that all the delivery points are known. A decision must then be made quickly (in practice, in less than ten minutes) on how to carry out the deliveries. Califrais has a fixed fleet that can be expanded as needed. Each vehicle can be either a heavy goods vehicle or a light commercial vehicle, each with a specific capacity. Solving the non-shared vehicle routing problem therefore involves deciding how many vehicles are needed to complete the route, which customers are assigned to each vehicle, and then in what order these customers should be visited. The choices are guided by cost minimization, which includes fixed vehicle rental costs and variable costs related to fuel consumption. Finally, deliveries must adhere to time slots defined by customers, and road traffic, which varies depending on the time of day in urban areas, must be taken into account.

teaching

Mathematics Teacher

Pre-Calculus and Geometry, Thang Tien Thang Long Education Joint Stock Company, 2023

Employment as a Mathematics teacher.