Related papers: Polygons as optimal shapes with convexity constrai…
A linear quadratic Dirichlet control problem posed on a possibly non-convex polygonal domain is analyzed. Detailed regularity results are provided in classical Sobolev (Slobodetskii) spaces. In particular, it is proved that in the presence…
We utilize the same technique as in [arXiv:2205.04254 (2022)] to provide some representations of polynomials non-negative on a basic semi-algebraic set, defined by polynomial inequalities, under more general conditions. Based on each…
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…
We present a hierarchy of semidefinite programs (SDPs) for the problem of fitting a shape-constrained (multivariate) polynomial to noisy evaluations of an unknown shape-constrained function. These shape constraints include convexity or…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
In this paper we address the following shape optimization problem: find the planar domain of least area, among the sets with prescribed constant width and inradius. In the literature, the problem is ascribed to Bonnesen, who proposed it in…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…
We consider shape functionals of the form $F_q(\Omega)=P(\Omega)T^q(\Omega)$ on the class of open sets of prescribed Lebesgue measure. Here $q>0$ is fixed, $P(\Omega)$ denotes the perimeter of $\Omega$ and $T(\Omega)$ is the torsional…
We consider an optimization problem with positively homogeneous functions in its objective and constraint functions. Examples of such positively homogeneous functions include the absolute value function and the $p$-norm function, where $p$…
In this paper, we investigate the concept of p-convexity for sets and functions in n-dimensional Euclidean space. We establish novel algebraic and topological results within this generalized convexity framework. Furthermore, we analyze…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
The Pompeiu problem is considered as shape optimization problem. We show stability of the ball which is the minimum point of related domain functional. The proof is based on shape derivative method. Stability of the ball for general domain…
The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the…
A small polygon is a polygon of unit diameter. The maximal perimeter and the maximal width of a convex small polygon with $n=2^s$ vertices are not known when $s \ge 4$. In this paper, we construct a family of convex small $n$-gons, $n=2^s$…
In this article we study convex integer maximization problems with composite objective functions of the form $f(Wx)$, where $f$ is a convex function on $\R^d$ and $W$ is a $d\times n$ matrix with small or binary entries, over finite sets…
We study nonconvex optimization landscapes for learning overcomplete representations, including learning (i) sparsely used overcomplete dictionaries and (ii) convolutional dictionaries, where these unsupervised learning problems find many…
We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point,…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…