Related papers: A perturbation view of level-set methods for conve…

We analyze stochastic conditional gradient methods for constrained optimization problems arising in over-parametrized machine learning. We show that one could leverage the interpolation-like conditions satisfied by such models to obtain…

In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…

Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…

We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…

In this paper, we exploit the so-called value function reformulation of the bilevel optimization problem to develop duality results for the problem. Our approach builds on Fenchel-Lagrange-type duality to establish suitable results for the…

Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…

In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…

We consider regularization methods based on the coupling of Tikhonov regularization and projection strategies. From the resulting constraint regularization method we obtain level set methods in a straight forward way. Moreover, we show that…

The present work illustrates a difficulty with the level-set method to accurately capture the curvature of interfaces in regions that are of equal distance to two or more interfaces. Such regions are characterized by kinks in the level-set…

We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…

Typically, the sequence of points generated by an optimization algorithm may have multiple limit points. Under convexity assumptions, however, (sub)gradient methods are known to generate a convergent sequence of points. In this paper, we…

The addition of lower level integrality constraints to a bi-level linear program is known to result in significantly weaker analytical properties. Most notably, the upper level goal function in the optimistic setting lacks lower…

Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…

The increasing availability of massive data sets poses a series of challenges for machine learning. Prominent among these is the need to learn models under hardware or human resource constraints. In such resource-constrained settings, a…

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…

Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…

This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…

We establish a maximum principle for a two-point function in order to analyze the convexity of level sets of harmonic functions. We show that this can be used to prove a strict convexity result involving the smallest principal curvature of…

In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from…

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…