Graphs of minimal point mappings of parametric optimization problems appear in the definition of feasible sets of bilevel optimization problems and of semi-infinite optimization problems, and the intersection of multiple such graphs defines (generalized) Nash equilibria. This paper shows how minimal point graphs of nonconvex parametric optimization problems can be written with the help of … 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
Positive spanning sets (PSSs) are families of vectors that span a given linear space through non-negative linear combinations. Despite certain classes of PSSs being well understood, a complete characterization of PSSs remains elusive. In this paper, we explore a relatively understudied relationship between positive spanning sets and strongly edge-connected digraphs, in that the former can … Read more
For verifying the safety of neural networks (NNs), Fazlyab et al. (2019) introduced a semidefinite programming (SDP) approach called DeepSDP. This formulation can be viewed as the dual of the SDP relaxation for a problem formulated as a quadratically constrained quadratic program (QCQP). While SDP relaxations of QCQPs generally provide approximate solutions with some gaps, … Read more
In this work, we propose a modification of Ryu’s splitting algorithm for minimizing the sum of three functions, where two of them are convex with Lipschitz continuous gradients, and the third is an arbitrary proper closed function that is not necessarily convex. The modification is essential to facilitate the convergence analysis, particularly in establishing a … Read more
In this paper we deal with the feasibility-seeking problem for unions of convex sets (UCS) sets and propose an iterative process for its solution. Renewed interest in this problem stems from the fact that it was recently discovered to serve as a modeling approach in fields of applications and from the ongoing recent research efforts … Read more
Derivative-free optimization algorithms are particularly useful for tackling blackbox optimization problems where the objective function arises from complex and expensive procedures that preclude the use of classical gradient-based methods. In contemporary decentralized environments, such functions are defined locally on different computational nodes due to technical or privacy constraints, introducing additional challenges within the optimization process. … Read more
We show that continuous quadratic submodular minimization with bounds is solvable in polynomial time using semidefinite programming, and we apply this result to two moment problems arising in distributionally robust optimization and the computation of covariance bounds. Accordingly, this research advances the ongoing study of continuous submodular minimization and opens new application areas therein. ArticleDownload … Read more
Inverse problems are inherently ill-posed, leading standard optimization techniques to fail and necessitating the use of regularization. This paper introduces a regularized, structure-exploiting Powell-Symmetric-Broyden method under modified secant conditions for solving ill-posed inverse problems in both infinite dimensional and finite dimensional settings. Our approach integrates regularization and structure exploitation directly within the Quasi-Newton framework, leveraging … Read more
Multiobjective blackbox optimization deals with problems where the objective and constraint functions are the outputs of a numerical simulation. In this context, no derivatives are available, nor can they be approximated by finite differences, which precludes the use of classical gradient-based techniques. The DMulti-MADS algorithm implements a state-of-the-art direct search procedure for multiobjective blackbox optimization … Read more