The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence results for CGM, the assumptions employed therein are quite restrictive; in some cases, certain assumptions are mutually inconsistent, leading to gaps in the underlying analysis. This … Read more
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework of quadratic penalty methods. Thus, depending on the problem at hand, the resulting method may exhibit a sample size strategy ranging from a mini-batch on one … Read more
In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially constructs increasingly accurate approximations of the true problems which are solved to a specified accuracy via a deterministic solver, thereby decoupling the uncertainty from … Read more
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic optimization method is proposed. The method belongs to the class of variable sample size first order methods, … Read more
This document presents a (mostly) chronologically-ordered bibliography of scientific publications on the superiorization methodology and perturbation resilience of algorithms which is compiled and continuously updated by us at: http://math.haifa.ac.il/yair/bib-superiorization-censor.html. Since the beginnings of this topic we try to trace the work that has been published about it since its inception. To the best of our … Read more
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy values of the objective and constraint functions and their first-order derivatives are available. The algorithm is based on a combination of a previously … Read more
In this paper, we propose a method that has foundations in the line search sequential quadratic programming paradigm for solving general nonlinear equality constrained optimization problems. The method employs a carefully designed modified line search strategy that utilizes second-order information of both the objective and constraint functions, as required, to mitigate the Maratos effect. Contrary … Read more
Derivative-based iterative methods for nonlinearly constrained non-convex optimization usually share common algorithmic components, such as strategies for computing a descent direction and mechanisms that promote global convergence. Based on this observation, we introduce an abstract framework based on four common ingredients that describes most derivative-based iterative methods and unifies their workflows. We then present Uno, … Read more
In this work, we propose the joint use of a mixed penalty-logarithmic barrier approach and generating set search, for addressing nonlinearly constrained derivative-free optimization problems. A merit function is considered, wherein the set of inequality constraints is divided into two groups: one treated with a logarithmic barrier approach, and another, along with the equality constraints, … Read more
Direct Multisearch (DMS) is a well-established class of methods for multiobjective derivative-free optimization, where constraints are addressed by an extreme barrier approach, only evaluating feasible points. In this work, we propose a filter approach, combined with an inexact feasibility restoration step, to address constraints in the DMS framework. The filter approach treats feasibility as an … Read more