In this paper we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates. Independently of how these iterates are computed, we prove that all accumulation points of the sequence generated by the algorithm are feasible. Computing the new iterates by the inexact restoration method, we prove … Read more
We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral stochastic finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem … Read more
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. Article Download View … Read more
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 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. Citation A.V. Dmitruk, A.M. Kaganovich. The Hybrid Maximum Principle is a consequence of Pontryagin Maximum Principle, Systems & Control … Read more
Recently Cambini and Carosi described a characterization of pseudolinearity of quadratic fractional functions. A reformulation of their result was given by Rapcsák. Using this reformulation, in this paper we describe an alternative proof of the Cambini–Carosi Theorem. Our proof is shorter than the proof given by Cambini–Carosi and less involved than the proof given by … Read more
We consider the question of global convergence of iterative methods for nonlinear programming problems. Traditionally, penalty functions have been used to enforce global convergence. In this paper we review a recent alternative, so-called filter methods. Instead of combing the objective and constraint violation into a single function, filter methods view nonlinear optimization as a biobjective … Read more
The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity, metric regularity along a subspace, strong metric regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version … Read more
This paper proposes a new stochastic algorithm, Search via Probability (SP) algorithm, for single-objective optimization problems. The SP algorithm uses probabilities to control the process of searching for optimal solutions. We calculate probabilities of the appearance of a better solution than the current one on each iteration, and on the performance of SP algorithm we … Read more
We study piecewise decomposition methods for mathematical programs with equilibrium constraints (MPECs) for which all constraint functions are linear. At each iteration of a decomposition method, one step of a nonlinear programming scheme is applied to one piece of the MPEC to obtain the next iterate. Our goal is to understand global convergence to B-stationary … Read more