Related papers: On error bounds and optimality conditions at infin…
Error bound analysis, which estimates the distance of a point to the solution set of an optimization problem using the optimality residual, is a powerful tool for the analysis of first-order optimization algorithms. In this paper, we use…
As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $\epsilon$-accurate…
The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the…
In this paper, we present some new necessary and sufficient optimality conditions in terms of the Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
We consider the unambiguous discrimination of multipartite quantum states and provide an upper bound for the maximum success probability of optimal local discrimination. We also provide a necessary and sufficient condition to realize the…
The aim of this paper is first to give necessary and sufficient condition of existence (of free boundaries) for both Laplacian and bi-Laplacian operators in the case where the overdetermined condition is not constant. second, by using some…
This article is devoted to the stability of error bounds (local and global) for semi-infinite convex constraint systems in Banach spaces. We provide primal characterizations of the stability of local and global error bounds when systems are…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
Direct and inverse initial-boundary problems on a bounded interval for systems of quasilinear evolution equations with general nonlinearities are considered. In the case of inverse problems conditions of integral overdetermination are…
Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For…
This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality.…
In this paper we consider an impulsive extension of an optimal control problem with unbounded controls, subject to endpoint and state constraints. We show that the existence of an extended-sense minimizer that is a normal extremal for a…
We investigate a limit value of an optimal control problem when the horizon converges to infinity. For this aim, we suppose suitable nonexpansive-like assumptions which does not imply that the limit is independent of the initial state as it…
Many optimization algorithms$\unicode{x2013}$including gradient descent, proximal methods, and operator splitting techniques$\unicode{x2013}$can be formulated as fixed-point iterations (FPI) of continuous operators. When these operators are…
This paper addresses a decision problem highlighted by Grigorchuk, Nekrashevich, and Sushchanskii, namely the finiteness problem for automaton (semi)groups. For semigroups, we give an effective sufficient but not necessary condition for…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
We consider an optimization problem subject to an abstract constraint and finitely many nonlinear constraints. Using the recently introduced concept of $n$-polyhedricity, we are able to provide second-order optimality conditions under weak…
Lasserre's hierarchy is a sequence of semidefinite relaxations for solving polynomial optimization problems globally. This paper studies the relationship between optimality conditions in nonlinear programming theory and finite convergence…
Generalized empirical likelihood and generalized method of moments are well spread methods of resolution of inverse problems in econometrics. Each method defines a specific semiparametric model for which it is possible to calculate…