Related papers: Optimization in Bochner Spaces
We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein…
Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…
We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite…
Convex optimization is crucial in controlling legged robots, where stability and optimal control are vital. Many control problems can be formulated as convex optimization problems, with a convex cost function and constraints capturing…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…
Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…
We study non-smooth stochastic decentralized optimization problems over time-varying networks, where objective functions are distributed across nodes and network connections may intermittently appear or break. Specifically, we consider two…
Counterexamples to some old-standing optimization problems in the smooth convex coercive setting are provided. We show that block-coordinate, steepest descent with exact search or Bregman descent methods do not generally converge. Other…
In this article, we develop an algorithm suitable for constrained optimization in $\mathbb{R}^n$. The results are developed through standard tools of n-dimensional real analysis and basic concepts of optimization. Indeed, the well known…
The integration of optimization problems within neural network architectures represents a fundamental shift from traditional approaches to handling constraints in deep learning. While it is long known that neural networks can incorporate…
In this paper we present an inexact zeroth-order method suitable for the solution nonsmooth and nonconvex stochastic composite optimization problems, in which the objective is split into a real-valued Lipschitz continuous stochastic…
This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are…
We use convex relaxation techniques to produce lower bounds on the optimal value of subset selection problems and generate good approximate solutions. We then explicitly bound the quality of these relaxations by studying the approximation…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces.…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…