Journal of Global Optimization
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Simple linkage: Analysis of a threshold-accepting global optimization method
Journal of Global Optimization - Tập 9 - Trang 95-111 - 1996
In a recent paper the authors introduced an infinite class of global optimization algorithms based upon random sampling from the feasible region and local searches started from selected sample points, based upon an acceptance/rejection criterion. All of the algorithms of that class possess strong theoretical properties. Here we analyze a member of that family, which, although being significantly s......
Augmented Lagrangian Duality and Nondifferentiable Optimization Methods in Nonconvex Programming
Journal of Global Optimization - - 2002
In this paper we present augmented Lagrangians for nonconvex minimization problems with equality constraints. We construct a dual problem with respect to the presented here Lagrangian, give the saddle point optimality conditions and obtain strong duality results. We use these results and modify the subgradient and cutting plane methods for solving the dual problem constructed. Algorithms proposed ......
A bisection-extreme point search algorithm for optimizing over the efficient set in the linear dependence case
Journal of Global Optimization - Tập 3 - Trang 95-111 - 1993
The algorithms and algorithmic ideas currently available for globally optimizing linear functions over the efficient sets of multiple objective linear programs either use nonstandard subroutines or cannot yet be implemented for lack of sufficient development. In this paper a Bisection-Extreme Point Search Algorithm is presented for globally solving a large class of such problems. The algorithm fin......
Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints
Journal of Global Optimization - Tập 49 - Trang 293-311 - 2010
This paper studies the relationship between the so-called bi-quadratic optimization problem and its semidefinite programming (SDP) relaxation. It is shown that each r-bound approximation solution of the relaxed bi-linear SDP can be used to generate in randomized polynomial time an
$${\mathcal{O}(r)}$$
-ap......
Application of the sequential parametric convex approximation method to the design of robust trusses
Journal of Global Optimization - Tập 68 - Trang 169-187 - 2016
We study an algorithm recently proposed, which is called sequential parametric approximation method, that finds the solution of a differentiable nonconvex optimization problem by solving a sequence of differentiable convex approximations from the original one. We show as well the global convergence of this method under weaker assumptions than those made in the literature. The optimization method i......
A New Class of Improved Convex Underestimators for Twice Continuously Differentiable Constrained NLPs
Journal of Global Optimization - - 2004
Survivable network design under optimal and heuristic interdiction scenarios
Journal of Global Optimization - Tập 38 - Trang 181-199 - 2006
We examine the problem of building or fortifying a network to defend against enemy attacks in various scenarios. In particular, we examine the case in which an enemy can destroy any portion of any arc that a designer constructs on the network, subject to some interdiction budget. This problem takes the form of a three-level, two-player game, in which the designer acts first to construct a network ......
Practical exponential set stabilization for switched nonlinear systems with multiple subsystem equilibria
Journal of Global Optimization - Tập 65 - Trang 109-118 - 2015
This paper studies the practical exponential set stabilization problem for switched nonlinear systems via a
$$\tau $$
-persistent approach. In these kinds of switched systems, every autonomous subsystem has one unique equilibrium point and these s......
ORCA: Outlier detection and Robust Clustering for Attributed graphs
Journal of Global Optimization - Tập 81 Số 4 - Trang 967-989 - 2021
Separating disconnected quadratic level sets by other quadratic level sets
Journal of Global Optimization - - Trang 1-27 - 2023
Given a quadratic function
$$f(x) = x^T A x + 2 a^T x + a_0$$
and its level sets, including
$$\{x\in \mathbb {R}^n \mid f(x) < 0\}$$
,
$$\{x\in \mathbb {R}^n \......
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