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In this article we provide examples, methods and algorithms to determine conditions on the parameters of certain type of parametric optimization problems, such that among the resulting local minima and maxima there is at least one which…
In this paper, we discuss a class of spectral partition problems with a measure constraint, for partitions of a given bounded connected open set. We establish the existence of an optimal open partition, showing that the corresponding…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems…
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range amongst those with unbalanced…
A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space.…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected)…
Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this…
A class of exact penalty-type local search methods for optimal control problems with nonsmooth cost functional, nonsmooth (but continuous) dynamics, and nonsmooth state and control constraints is presented, in which the the penalty…
The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only…
In this paper, we study possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general nonlinear and nonsmooth cone constrained optimization…
Penalty functions or regularization terms that promote structured solutions to optimization problems are of great interest in many fields. Proposed in this work is a nonconvex structured sparsity penalty that promotes one-sparsity within…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
Consider the regularized sparse minimization problem, which involves empirical sums of loss functions for $n$ data points (each of dimension $d$) and a nonconvex sparsity penalty. We prove that finding an…
We discuss removability problems concerning differentiability and pointwise Lipschitz conditions for functions of a real variable. We prove that, in each of the settings under consideration, a set is removable if and only if it has no…
The paper addresses general constrained and non-linear optimization problems. For some of these notoriously hard problems, there exists a reformulation as an unconstrained, global optimization problem. We illustrate the transformation, and…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…