Many applications from various fields can be modeled as problems involving the minimization of a function, such as distance or cost. Multi-objective optimization is a sub-area of optimization in the broadest sense, where not one but several functions have to be minimized simultaneously.
“The typical example is that given by Nobel Prize winner Henry Markowitz in which an investor wants to both maximize profit and limit risk,” explains Sorin-Mihai Grad. “New solution concepts had to be invented for this, these problems becoming increasingly complex. Nowadays, it's becoming essential to solve these problems using algorithms, iterative schemes that practitioners (like machine learning people) will be able to use to carry out these multi-objective optimizations successfully and within reasonable timescales.”
Sorin-Mihai Grad presented at the conference the fruit of a long-standing collaboration with Hungarian colleagues, proposing the first exact algorithm known in the literature for iteratively solving differentiable multi-objective optimization problems. More precisely, his talk discussed an original approach based on linear optimization that offers a mathematical guarantee of convergence of the proposed algorithms without the need for heuristic solvers.
Sorin-Mihaï Grad joined ENSTA Paris from the University of Vienna in October 2021, to strengthen the “Optimization and Control” team in the Applied Mathematics Unit, and is delighted to have been selected for this teaching-research position.
