Related papers: Compensated Convexity on Bounded Domains, Mixed Mo…
We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them…
This paper presents a family of algorithms for decentralized convex composite problems. We consider the setting of a network of agents that cooperatively minimize a global objective function composed of a sum of local functions plus a…
The Bregman proximal mapping and Bregman-Moreau envelope are traditionally studied for functions defined on the entire space $\mathbb{R}^n$, even though these constructions depend only on the values of the function within (the interior of)…
In this work the minimization problem for the difference of convex (DC) functions is studied by using Moreau envelopes and the descent method with Moreau gradient is employed to approximate the numerical solution. The main regularization…
In this work, we introduce a new class of non-convex functions, called implicit concave functions, which are compositions of a concave function with a continuously differentiable mapping. We analyze the properties of their minimization by…
Chance-constrained programming is a widely used framework for decision-making under uncertainty, yet its mixed-integer reformulations involve nonconvex mixing sets with a knapsack constraint, leading to weak relaxations and computational…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
In this work, we propose a detailed computational framework for modelling the envelope of the swept volume, that is the boundary of the volume obtained by sweeping an input solid along a trajectory of rigid motions. Our framework is adapted…
Minimax optimization has become a central tool in machine learning with applications in robust optimization, reinforcement learning, GANs, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify…
This paper aims to study the dual of an extended locally convex space. In particular, we study the weak and weak* topologies as well as the topology of uniform convergence on bounded subsets of an extended locally convex space. As an…
This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
This paper presents a novel framework for nonconvex enhancement of minimization induced (MI) penalties while preserving the overall convexity of associated regularization models. MI penalties enable the adaptation to certain signal…
For many applications, we need to use techniques to represent convex shapes and objects. In this work, we use level set method to represent shapes and find a necessary and sufficient condition on the level set function to guarantee the…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…
Many tasks in image processing can be tackled by modeling an appropriate data fidelity term $\Phi: \mathbb{R}^n \rightarrow \mathbb{R} \cup \{+\infty\}$ and then solve one of the regularized minimization problems \begin{align*}…
Introduced in the 1960s, the Moreau envelope has grown to become a key tool in non\-smooth analysis and optimization. Essentially an infimal convolution with a parametrized norm squared, the Moreau envelope is used in many applications and…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
In the optimization of convex domains under a PDE constraint numerical difficulties arise in the approximation of convex domains in $\mathbb{R}^3$. Previous research used a restriction to rotationally symmetric domains to reduce shape…