Related papers: On Subdifferentials Via a Generalized Conjugation …
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.,…
In this paper, we consider solving a composite optimization problem with coupling constraints in a multi-agent network based on proximal gradient method. In this problem, all the agents jointly minimize the sum of individual cost functions…
In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…
In this work, for an equation of high even order with a fractional derivative in the sense of Caputo, a problem is studied in a rectangular domain with conjugation conditions. A criterion for the uniqueness of a solution is given. The…
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.This fact motivates the consideration of subdifferentials for such typically just continuous…
Abstract Equivalent conditions that make the convex subdifferential maximal monotone are investigated in the general settings of locally convex spaces.
In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the…
We link regularity and smoothness analysis of multivariate vector subdivision schemes with network flow theory and with special linear optimization problems. This connection allows us to prove the existence of what we call optimal…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
In this paper, we consider the convex, finite-sum minimization problem with explicit convex constraints over strongly connected directed graphs. The constraint is an intersection of several convex sets each being known to only one node. To…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
In this paper, we present the concept of subdifferential for fuzzy n-cell number valued functions. Then we state some theorems related to subdifferentiability based on the new definition. Finally, we present some applications emphasized on…
The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, particularly in the context of nonsmooth optimization. The present work proposes…
The conjugate gradient method (CG) is typically used with a preconditioner which improves efficiency and robustness of the method. Many preconditioners include parameters and a proper choice of a preconditioner and its parameters is often…
Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial…
In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…
We investigate a novel characteristic of the conjugate function associated to a generic convex optimization problem, which can subsequently be leveraged for efficient dual decomposition methods. In particular, under mild assumptions, we…
A unified framework to derive optimized compact schemes for a uniform grid is presented. The optimal scheme coefficients are determined analytically by solving an optimization problem to minimize the spectral error subject to equality…
Subdifferentials (in the sense of convex analysis) of matrix-valued functions defined on $\mathbb{R}^d$ that are convex with respect to the L\"{o}wner partial order can have a complicated structure and might be very difficult to compute…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…