Related papers: On optimization on ravine functions. Minkowski-Coh…
In this paper, we are interested in shape optimization problems involving the ge ometry (normal, curvatures) of the surfaces. We consider a class of hypersurface s in $\mathbb{R}^{n}$ satisfying a uniform ball condition and we prove the…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
A framework is presented whereby a general convex conic optimization problem is transformed into an equivalent convex optimization problem whose only constraints are linear equations and whose objective function is Lipschitz continuous.…
A natural kind of compactification of the virtual moduli spaces of rational functions of one complex variable is given. To describe the boundary points geometrically, the authors introduce the concept of rational functions with nodes,…
Gradient flows are a powerful tool for optimizing functionals in general metric spaces, including the space of probabilities endowed with the Wasserstein metric. A typical approach to solving this optimization problem relies on its…
In this paper, we perform a rigourous version of shape and topological derivatives for optimizations problems under constraint Helmoltz problems. A shape and topological optimization problem is formulated by introducing cost functional. We…
We introduce canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space and prove the existence and the uniqueness of these parameters. With respect to these coordinates the coefficients of the first…
The paper is devoted to the study of regularized versions of multiobjective optimization problems described by directionally Lipschitzian functions. Such regularizations appear in proximal-type algorithms of multiobjective optimization,…
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g.,…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
Riemannian structures on infinite-dimensional manifolds arise naturally in shape analysis and shape optimization. These applications lead to optimization problems on manifolds which are not modeled on Banach spaces. The present article…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
In this paper, we mainly study solution uniqueness of some convex optimization problems. Our characterizations of solution uniqueness are in terms of the radial cone. This approach allows us to know when a unique solution is a strong…
Using the weak solution of Inverse mean curvature flow, we prove the sharp Minkowski-type inequality for outward minimizing hypersurfaces in Schwarzschild space.
The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…
We perform a systematic study of optimization problems in the Wasserstein spaces that are analogs of infinite horizon, deterministic control problems. We derive necessary conditions on action minimizing paths and present a sufficient…
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…