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We study bilevel optimization problems where the lower-level problems are strongly convex and have coupled linear constraints. To overcome the potential non-smoothness of the hyper-objective and the computational challenges associated with…
Model Predictive Control (MPC) is a common tool for the control of nonlinear, real-world systems, such as legged robots. However, solving MPC quickly enough to enable its use in real-time is often challenging. One common solution is given…
Bilevel optimization has garnered significant attention in the machine learning community recently, particularly regarding the development of efficient numerical methods. While substantial progress has been made in developing efficient…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
Learning approaches rely on hyperparameters that impact the algorithm's performance and affect the knowledge extraction process from data. Recently, Nonnegative Matrix Factorization (NMF) has attracted a growing interest as a learning…
Common computational problems, such as parameter estimation in dynamic models and PDE constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive…
Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine…
In this paper, we studied the federated bilevel optimization problem, which has widespread applications in machine learning. In particular, we developed two momentum-based algorithms for optimizing this kind of problem and established the…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
In this study, we introduce a novel methodological framework called Bayesian Penalized Empirical Likelihood (BPEL), designed to address the computational challenges inherent in empirical likelihood (EL) approaches. Our approach has two…
Bilevel optimization involves a hierarchical structure where one problem is nested within another, leading to complex interdependencies between levels. We propose a single-loop, tuning-free algorithm that guarantees anytime feasibility,…
This paper studies bilevel polynomial optimization in which lower-level constraint functions depend linearly on lower-level variables. We show that such bilevel program can be reformulated as a disjunctive program by using…
We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…
In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…
We introduce the Morse parametric qualification condition for bilevel programming. Generic semi-algebraic functions are Morse parametric in a piecewise sense. Thus, bilevel programs with a Morse parametric lower level constitute a relevant…
We investigate numerically the optimal constants in Lieb-Thirring inequalities by studying the associated maximization problem. We use a monotonic fixed-point algorithm and a finite element discretization to obtain trial potentials which…
Stochastic bilevel optimization generalizes the classic stochastic optimization from the minimization of a single objective to the minimization of an objective function that depends the solution of another optimization problem. Recently,…
In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…
When the lower-level optimal solution set-valued mapping of a bilevel optimization problem is not single-valued, we are faced with an ill-posed problem, which gives rise to the optimistic and pessimistic bilevel optimization problems, as…
Bilevel optimization (BO) has recently gained prominence in many machine learning applications due to its ability to capture the nested structure inherent in these problems. Recently, many hypergradient methods have been proposed as…