In the first part of this paper, we prove a minimax inequality for maps satisfying a generalized coercivity type condition. As a consequence, we prove a result on the solvability of complementarity problems. In the second part, a result on the existence of maximal element in non-compact domains is obtained and as application, we prove the existence of equilibrium for an abstract economy (or gen...

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions global stability a positive solution for delayed feedback Gilpin–Ayala competition model with disturbance. The conclusion obtained in this reduces conservatism algorithm compared known literature, disturbance is not limited control.

We give a comprehensive theoretical characterization of a nonparametric estimator for the L2 divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is √ n-consistent provided the densities are sufficiently smooth. In this smooth regime, we then show that our estimator is asymptotically normal, construct asymptotic confidence int...

In this paper, the authors prove some existence results of solutions for a new class of generalized quasi-variational inequalities (GQVI) for pseudo-monotone type III operators and strongly pseudo-monotone type III operators defined on noncompact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GQVI for pseudo-monotone type III operators, we shall use Ch...

This paper studies sparse density estimation via l1 penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities and that it yields minimax adaptive density estimates. These results are based on a g...

We prove some existence results of solutions for a new class of generalized bi-quasivariational inequalities GBQVI for quasi-pseudomonotone type II and strongly quasi-pseudomonotone type II operators defined on noncompact sets in locally convex Hausdorff topological vector spaces. To obtain these results on GBQVI for quasi-pseudomonotone type II and strongly quasipseudomonotone type II operator...

Consider the standard linear regression model Y = Xβ+w, where Y ∈ R is an observation vector, X ∈ R is a design matrix, β ∈ R is the unknown regression vector, and w ∼ N (0,σI) is additive Gaussian noise. This paper studies the minimax rates of convergence for estimation of β for #p-losses and in the #2-prediction loss, assuming that β belongs to an #q-ball Bq(Rq) for some q ∈ [0, 1]. We show t...

Consider the standard linear regression model Y = Xβ+w, where Y ∈ R is an observation vector, X ∈ R is a design matrix, β ∈ R is the unknown regression vector, and w ∼ N (0, σI) is additive Gaussian noise. This paper studies the minimax rates of convergence for estimation of β for lp-losses and in the l2-prediction loss, assuming that β belongs to an lq-ball Bq(Rq) for some q ∈ [0, 1]. We show ...

We present a new version of first order necessary optimality conditions for a static minmax problem with inequality constraints in the parametric constraint case. These conditions, after some modification, turn out to characterize strict local minimizers of order one for the given problem.

ABSTRACT. Let R be a commutative noetherian ring, I and J are two ideals of R. Inthis paper we introduce the concept of (I;J)- minimax R- module, and it is shown thatif M is an (I;J)- minimax R- module and t a non-negative integer such that HiI;J(M) is(I;J)- minimax for all i