We study a set of regularization methods for high-dimensional linear regression models. These penalized estimators have the square root of the residual sum of squared errors as loss function, and any weakly decomposable norm as penalty function. This fit measure is chosen because of its property that the estimator does not depend on the unknown standard deviation of the noise. On the other hand...

In this article we define certain conditions on the functionals of multi-objective fractional variational problem in order that it becomes F-Kuhn Tucker pseudo invex or F-Fritz John pseudo invex. We also define F-KT and F-FJ points. Further, these problems are characterized such that all F-KT and F-FJ points become efficient solutions for the featured problem. An example is presented to verify ...

Abstract: The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor is considered, and necessary optimality conditions are estabilished in a case where this conformal factor favours the spreading of the probability measure along the curve. These conditions have the form of a system of PDEs of the kind of the compressible Euler equations. Moreover, self-similar sol...

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar’s constraint qualification holds, which is called the “sum problem”. In this paper, we establish the maximal monotonicity of A+ B provided that A and B are maximally monotone operators such that domA ∩ int domB 6= ∅,...

The effects of priming are not limited to semantics but have also been witnessed in visual-motor tasks (Tucker & Ellis, 2001). By generalizing ACT-R’s (Anderson, 2007) existing spreading activation account to include visual representations and broadening the context within which associations are established, we have been able to replicate this small but reliable phenomenon both in simulation an...

We study second-order optimality conditions for mathematical programs with equilibrium constraints (MPEC). Firstly, we improve some second-order optimality conditions for standard nonlinear programming problems using some newly discovered constraint qualifications in the literature, and apply them to MPEC. Then, we introduce some MPEC variants of these new constraint qualifications, which are a...

JuFang Wang,* Erhe Gao,* Joseph Rabinowitz, Jianliang Song, Xue-Qian Zhang, Walter J. Koch, Amy L. Tucker, Tung O. Chan, Arthur M. Feldman, Joseph Y. Cheung Division of Nephrology and Center of Translational Medicine, Department of Medicine, Jefferson Medical College, Thomas Jefferson University, Philadelphia, Pennsylvania; and Cardiovascular Division, Department of Internal Medicine, Universit...

This paper deals with optimality conditions to solve nonlinear programming problems. The classical Karush-Kuhn-Tucker (KKT) optimality conditions are demonstrated through a cone approach, using the well known Farkas’ Lemma. These conditions are valid at a minimizer of a nonlinear programming problem if a constraint qualification is satisfied. First we prove the KKT theorem supposing the equalit...

The positive semidefinite rank of a convex body C is the size of its smallest positive semidefinite formulation. We show that the positive semidefinite rank of any convex body C is at least √ log d where d is the smallest degree of a polynomial that vanishes on the boundary of the polar of C. This improves on the existing bound which relies on results from quantifier elimination. Our proof reli...

We first introduce a new notion of the partial and generalized cone subconvexlike set-valued map and give an equivalent characterization of the partial and generalized cone subconvexlike set-valued map in linear spaces. Secondly, a generalized alternative theorem of the partial and generalized cone subconvexlike set-valued map was presented. Finally, Kuhn-Tucker conditions of set-valued optimiz...