We propose a general framework for analyzing and developing fully corrective boosting-based classifiers. The framework accepts any convex objective function, and allows any convex (for example, ℓp-norm, p ≥ 1) regularization term. By placing the wide variety of existing fully corrective boosting-based classifiers on a common footing, and considering the primal and dual problems together, the fr...

Using a regularized Nikaido-Isoda function, we present a (nonsmooth) constrained optimization reformulation of a class of generalized Nash equilibrium problems (GNEPs). Further we give an unconstrained reformulation of a large subclass of all GNEPs which, in particular, includes the jointly convex GNEPs. Both approaches characterize all solutions of a GNEP as minima of optimization problems. Th...

It is well known that quadrant dependent (QD) random variables are also quadrant dependent in expectation (QDE). Recent literature has offered examples rigorously establishing the fact that there are QDE random variables which are not QD. The examples are based on convex combinations of specially chosen QD copulas: one negatively QD and another positively QD. In this paper we establish general ...

This paper concerns maximal flows on Z traveling from a convex set to infinity, the flows being restricted by a random capacity. For every compact convex set A, we prove that the maximal flow Φ(nA) between nA and infinity is such that Φ(nA)/n almost surely converges to the integral of a deterministic function over the boundary of A. The limit can also be interpreted as the optimum of a determin...

We describe an asynchronous parallel stochastic proximal coordinate descent algorithm for minimizing a composite objective function, which consists of a smooth convex function plus a separable convex function. In contrast to previous analyses, our model of asynchronous computation accounts for the fact that components of the unknown vector may be written by some cores simultaneously with being ...

This paper is concerned with the homogenization of the Dirichlet eigenvalue problem, posed in a bounded domain Ω ⊂ R, for a vectorial elliptic operator −∇·A(·)∇ with ε-periodic coefficients. We analyse the asymptotics of the eigenvalues λ when ε → 0, the mode k being fixed. A first-order asymptotic expansion is proved for λ in the case when Ω is either a smooth uniformly convex domain, or a con...

Consider L being a continuous lattice, two functors from the category of convex spaces (denoted by CS) to the category of stratified L-convex spaces (denoted by SL-CS) are defined. The first functor enables us to prove that the category CS can be embedded in the category SL-CS as a reflective subcategory. The second functor enables us to prove that the category CS can be embedded in the categor...

Abstract. We consider 3-monotone approximation by piecewise polynomials with prescribed knots. A general theorem is proved, which reduces the problem of 3-monotone uniform approximation of a 3-monotone function, to convex local L1 approximation of the derivative of the function. As the corollary we obtain Jackson-type estimates on the degree of 3-monotone approximation by piecewise polynomials ...

This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained 2-block convex composite optimization problems with each block in the objective being the sum of a non-smooth convex function (p(x) or q(y)) and a smooth convex function (f(x) or g(y)), i.e., minx∈X , y∈Y{p(x) + f(x) + q(y) + g(y) | A∗x + B∗y = c}. B...

In this paper, we consider a type of cone-constrained convex program in finitedimensional space, and are interested in characterization of the solution set of this convex program with the help of the Lagrange multiplier. We establish necessary conditions for a feasible point being an optimal solution. Moreover, some necessary conditions and sufficient conditions are established which simplifies...