Necessary Optimality Conditions for Nonlinear Programming are discussed in the present research. A new Second-Order condition is given, which depends on a weak constant rank constraint requirement. We show that practical and publicly available algorithms (www.ime.usp.br/~egbirgin/tango) of Augmented Lagrangian type converge, after slight modifications, to stationary points defined by the new condition. ArticleDownload View PDF
We present an algorithm for large-scale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for large-scale applications for which the iteration matrix cannot be explicitly formed or factored and the arising linear systems must be solved … Read more
We show the linear convergence of a simple first-order algorithm for the minimum-volume enclosing ellipsoid problem and its dual, the D-optimal design problem of statistics. Computational tests confirm the attractive features of this method. CitationOptimization Methods and Software 23 (2008), 5–19. ArticleDownload View PDF
We propose an approach to the classical newsvendor problem and its extensions subject to uncertain demand that: (a) works directly with data, i.e., combines historical data and optimization in a single framework, (b) yields robust solutions and incorporates risk preferences using one scalar parameter, rather than utility functions, (c) allows for tractable formulations, specifically, linear … Read more
Dini derivative on Riemannian manifold setting is studied in this paper. In addition, a characterization for Lipschitz and convex functions defined on Riemannian manifolds and sufficient optimality conditions for constraint optimization problems in terms of the Dini derivative are given. ArticleDownload View PDF
The Flow Shop Problem (FSP) is known to be NP-hard when more than three machines are considered. Thus, for non-trivial size problem instances, heuristics are needed to find good orderings. We consider the permutation case of this problem. For this case, denoted by F|prmu|Cmax, the sequence of jobs has to remain the same at each … Read more
We study the set $S = \{(x, y) \in \Re_{+} \times Z^{n}: x + B_{j} y_{j} \geq b_{j}, j = 1, \ldots, n\}$, where $B_{j}, b_{j} \in \Re_{+} – \{0\}$, $j = 1, \ldots, n$, and $B_{1} | \cdots | B_{n}$. The set $S$ generalizes the mixed-integer rounding (MIR) set of Nemhauser and Wolsey and … Read more
This paper proposes a filter method for solving nonlinear semidefinite programming problems. Our method extends to this setting the filter SQP (sequential quadratic programming) algorithm, recently introduced for solving nonlinear programming problems, obtaining their respective global convergence results. CitationCMM-B-06/10 – 171 Centre for Mathematical Modelling, UMR 2071, Universidad de Chile-CNRS. Casilla 170-3 Santiago 3, Chile … Read more
A method for finding all roots of a system of nonlinear equations is described. Our method makes use of C-GRASP, a recently proposed continuous global optimization heuristic. Given a nonlinear system, we solve a corresponding adaptively modified global optimization problem multiple times, each time using C-GRASP, with areas of repulsion around roots that have already … Read more
We give a simple proof of the Maximum Principle for smooth hybrid control systems by reducing the hybrid problem to an optimal control problem of Pontryagin type and then by using the classical Pontryagin Maximum Principle. CitationA.V. Dmitruk, A.M. Kaganovich. The Hybrid Maximum Principle is a consequence of Pontryagin Maximum Principle, Systems & Control Letters, … Read more