Related papers: A Generalized Worst-Case Complexity Analysis for N…
In this paper, we propose a new non-monotone line-search method for smooth unconstrained optimization problems with objective functions that have many non-global local minimizers. The method is based on a relaxed Armijo condition that…
We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. Progress is measured by the Pareto stationarity gap $\mathcal{G}(x)$, the norm of the best convex…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
This paper addresses some trust-region methods equipped with nonmonotone strategies for solving nonlinear unconstrained optimization problems. More specifically, the importance of using nonmonotone techniques in nonlinear optimization is…
This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with…
Non-locality is the phenomenon of observing strong correlations among the outcomes of local measurements of a multipartite physical system. No-signaling boxes are the abstract objects for studying non-locality, and wirings are local…
We investigate the generalization ability of a simple perceptron trained in the off-line and on-line supervised modes. Examples are extracted from the teacher who is a non-monotonic perceptron. For this system, difficulties of training can…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent,…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
In this work, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of linear optimization over the subset of vertices of P that are not contained in X. This…
Topology optimization (TO) can be viewed as seeking an optimal solution in the design space of a given TO problem. For weakly non-linear TO problems, e.g., compliance minimization, sensitivity-based methods typically converge well, whereas…
In this work, we consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution $p$ over a poset is monotone if, for any pair of domain elements $x$ and $y$ such that $x \preceq y$,…
Local search is a powerful heuristic in optimization and computer science, the complexity of which has been studied in the white box and black box models. In the black box model, we are given a graph $G = (V,E)$ and oracle access to a…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
In this paper, we consider mixed-integer nonsmooth constrained optimization problems whose objective/constraint functions are available only as the output of a black-box zeroth-order oracle (i.e., an oracle that does not provide derivative…
In many practical applications, heuristic or approximation algorithms are used to efficiently solve the task at hand. However their solutions frequently do not satisfy natural monotonicity properties of optimal solutions. In this work we…