In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex convex optimization, with a focus on addressing constrained high-dimensional setting, saddle point avoiding. To handle first generalizations of the conditional gradient algorithm achieving rates similar to standard using only information. facilitate optimization in high dimensions, explore advan...

It is known that one can fold a convex polyhedron from a non-overlapping face unfolding, but the complexity of the algorithm in [MP] remains an open problem. In this paper we show that every convex polyhedron P ⊂ R can be obtained in polynomial time, by starting with a cube which contains P and sequentially cutting out the extra parts of the surface. Our main tool is of independent interest. We...

BACKGROUND Hepatitis C viral (HCV) load detection and quantification is routinely accomplished by HCV RNA measurement, an expensive but essential test, both for the diagnosis and treatment of chronic hepatitis C (CHC). HCV core antigen (Ag) testing has been suggested as an attractive alternative to molecular diagnostics. The aim of the study was to evaluate an automated chemiluminescent immunoa...

One can endow a matrix algebra M with the trace norm to obtain a finite dimensional Banach space L(M). Given two matrix algebras M1, M2, the natural inclusion of L 1(M1⊗M2) in the projective tensor product of Banach spaces L1(M1)⊗̂L 1(M2) is a bijection but not an isometry; and the projective cross norm can be restricted to the convex set S of density matrices in M1 ⊗ M2 to obtain a continuous c...

in this paper, we first introduce the notion of $c$-affine functions for $c> 0$.then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. moreover, a hyers–-ulam stability result for strongly convex functions is shown.

converges for x ∈ [0,∞). This tells us that f ∈ C[[0,∞)] if and only if it is a Laplace transform of the measure α. There have been a lot of literature about the completely monotonic functions, for examples, [3, 4, 5, 22, 25, 32, 34, 35, 39, 40, 42, 58, 60, 61, 62, 63, 66] and references therein. Recall also [6, 43, 47] that a positive function f is said to be logarithmically completely monoton...

Let X1, . . . ,Xn be independent and identically distributed random vectors with a (Lebesgue) density f. We first prove that, with probability 1, there is a unique log-concave maximum likelihood estimator f̂n of f. The use of this estimator is attractive because, unlike kernel density estimation, the method is fully automatic, with no smoothing parameters to choose. Although the existence proof ...

The analysis of flow in water-distribution networks with several pumps by the Content Model may be turned into a non-convex optimization uncertain problem with multiple solutions. Newton-based methods such as GGA are not able to capture a global optimum in these situations. On the other hand, evolutionary methods designed to use the population of individuals may find a global solution even for ...