By virtue of convexification techniques, we study best approximations to a closed set C in a Hilbert space as well as perturbation conditions relative to C and a nonlinear inequality system. Some results on equivalence of the best approximation and the basic constraint qualification are established.

Recently, a number of authors have presented several geometries for rankstructured matrix and tensor spaces, namely the set of matrices or tensors with fixed matrix, Tucker or TT rank. In this talk we present a unifying approach for establishing a smooth, differential structure on the set of tensors with fixed hierarchical Tucker rank. Our approach describes this set as a smooth submanifold, gl...

The Gibbs conditions of stable thermodynamic equilibrium are formulated for nonlinear thermoelastic materials, based on the constrained minimization of four fundamental thermodynamic potentials. Sufficient conditions for incremental stability are stated in each case. The previously unexplored connections between the second-order variations of thermodynamic potentials are used to establish the c...

A new algorithm is presented to solve both the finitehorizon time-varying and infinite-horizon timeinvariant discrete-time optimal reduced-order linear quadratic Gaussian (LQG) problem. In both cases the first order necessary optimality conditions can be represented by two non-linearly coupled discrete-time Lyapunov equations, which run forward and backward in discrete time. The algorithm itera...

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...