Cutting Plane Oracles to Minimize Non-smooth Non-convex Functions

Cutting plane oracles to minimize non-smooth non-convex functions

We discuss a bundle method for non-smooth non-convex optimization programs. In the absence of convexity, a substitute for the cutting plane mechanism has to be found. We propose such a mechanism and prove convergence of our method in the sense that every accumulation point of the sequence of serious iterates is critical.

Online Non-clairvoyant Scheduling to Simultaneously Minimize All Convex Functions

We consider scheduling jobs online to minimize the objective ∑ i∈[n] wig(Ci− ri), where wi is the weight of job i, ri is its release time, Ci is its completion time and g is any non-decreasing convex function. Previously, it was known that the clairvoyant algorithm Highest-DensityFirst (HDF) is (2 + )-speed O(1)-competitive for this objective on a single machine for any fixed 0 < < 1 [21]. We s...

On Non-smooth Convex Distance Functions

non-corrective approach to pronunciation

the aim of this study has been to find answers for the following questions: 1. what is the effect of immediate correction on students pronunciation errors? 2. what would be the effect of teaching the more rgular patterns of english pronunciation? 3. is there any significant difference between the two methods of dealing with pronuciation errore, i. e., correction and the teaching of the regular ...

Approximating convex functions via non-convex oracles under the relative noise model

We study succinct representations of a convex univariate function φ over a finite domain. We show how to construct a succinct representation, namely a piecewise-linear function φ̄ approximating φ when given a black box access to an L-approximation oracle φ̃ of φ (the oracle value is always within a multiplicative factor L from the true value). The piecewise linear function φ̄ has few breakpoints (...