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...

In this paper, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate the structure of both – the lower level equilibrium solution and objective integrand. We show almost sure convergence of optimal values, optimal solutions (both local and global) and general...

In this paper we study first order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend various wellknown constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs take...

Abstract In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the boundary satisfying the Gamma conditions of Lions. We will then consider two applications. The first one deals with the exact controllability problem for the wave equation with potential. Following the duality m...

Error bounds for cone inclusion problems in Banach spaces are established under conditions weaker than Robinson’s constraint qualification. The results allow the cone to be more general than the origin and therefore also generalize a classical error bound result concerning equality-constrained sets in optimization. Applications in finite-dimensional differentiable inequalities and in tangent co...

We provide new conditions for identification in accelerated failure time competing risks models. In our model, we specify unknown regression functions and the joint survivor function of latent disturbance terms nonparametrically. We show that the model can be identified with covariates that are independent of latent errors, provided that certain rank conditions are satisfied. We present a simpl...

We prove necessary optimality conditions for problems of the calculus of variations on time scales with a Lagrangian depending on the free end-point.

We obtain the necessary and sufficient conditions for linearizability of an eight-parameter family of two-dimensional system of differential equations in the form of linear canonical saddle perturbed by polynomials with four quadratic and four cubic terms. 2007 Elsevier Inc. All rights reserved.

We provide necessary optimality conditions for a general class of discounted infinitehorizon dynamic optimization problems. As part of the resulting maximum principle we obtain explicit bounds on the adjoint variable, stronger than the transversality conditions in Arrow–Kurz form. r 2005 Elsevier B.V. All rights reserved. JEL classification: C60; C61

We consider a (finite or infinite) family of closed convex sets with nonempty intersection in a normed space. A property relating their epigraphs with their intersection’s epigraph is studied, and its relations to other constraint qualifications (such as the linear regularity, the strong CHIP, and Jameson’s (G)-property) are established. With suitable continuity assumption we show how this prop...