This paper presents a methodology for using varying sample sizes in batch-type optimization methods for large scale machine learning problems. The first part of the paper deals with the delicate issue of dynamic sample selection in the evaluation of the function and gradient. We propose a criterion for increasing the sample size based on variance … Read more
The family of optimization problems with value function objectives includes the minmax programming problem and the bilevel optimization problem. In this paper, we derive necessary optimality conditions for this class of problems. The main focus is on the case where the functions involved are nonsmooth and the constraints are the very general operator constraints. CitationsubmittedArticleDownload … Read more
We propose a method to reduce the sizes of SDP relaxation problems for a given polynomial optimization problem (POP). This method is an extension of the elimination method for a sparse SOS polynomial in [Kojima et al., Mathematical Programming] and exploits sparsity of polynomials involved in a given POP. In addition, we show that this … Read more
Tressler’s Theorem states that the long-standing Hadamard conjecture (concerning the existence of n by n orthogonal matrices with elements of the same absolute value, for n=4k, k=1,2,…) will be settled if we find n-2 pairwise orthogonal words in a hyperplane of words. In this paper we will prove the counterpart of Tressler’s Theorem: the existence … Read more
Due to intrinsic complexity and sophistication of decision problems in tourism and recreation, respective decision making processes can not be implemented without making use of modern computer technologies and operations research approaches. In this paper, we review research works on modeling recreational systems. CitationAnnals of Operations Research (accepted)ArticleDownload View PDF
This paper takes a uniform look at the customized applications of proximal point algorithm (PPA) to two classes of problems: the linearly constrained convex minimization problem with a generic or separable objective function and a saddle-point problem. We model these two classes of problems uniformly by a mixed variational inequality, and show how PPA with … Read more
We present the formulation and analysis of a new sequential quadratic programming (\SQP) method for general nonlinearly constrained optimization. The method pairs a primal-dual generalized augmented Lagrangian merit function with a \emph{flexible} line search to obtain a sequence of improving estimates of the solution. This function is a primal-dual variant of the augmented Lagrangian proposed … Read more
The corner relaxation of a mixed-integer linear program is a central concept in cutting plane theory. In a recent paper Fischetti and Monaci provide an empirical assessment of the strength of the corner and other related relaxations on benchmark problems. In this paper we give a precise characterization of the bounds given by these relaxations … Read more
We relate a deterministic Kalman filter on semi-infinite interval to linear-quadratic tracking control model with unfixed initial condition CitationTechnical report, University of Notre Dame, October, 2011ArticleDownload View PDF
We propose a framework of lower bounds for the asymmetric traveling salesman problem (TSP) based on approximating the dynamic programming formulation with diff erent basis vector sets. We discuss how several well-known TSP lower bounds correspond to intuitive basis vector choices and give an economic interpretation wherein the salesman must pay tolls as he travels between … Read more