In the convex [[optimisation method]], we use a convex surrogate $\ell$ of the 0-1 loss function. $$\arg \min_{h \in H} \frac{1}{n} \sum_{i=1}^n l(X_i, Y_i, h) $$ This is because the 0-1 loss function ...

Given x 0 , a point of a convex subset C of a Euclidean space, the two following statements are proven to be equivalent: (i) every convex function f : C → ℝ is upper semi-continuous at x 0 , and (ii) ...

Convex optimisation constitutes a fundamental area in applied mathematics where the objective is to identify the minimum of a convex function subject to a set of convex constraints. This framework ...

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1 Russian-Armenian (Slavonic) University, Yerevan, Armenia. 2 Institute of Mathematics Armenian Academy of Sciences, Yerevan, Armenia. The problem of reconstruction of a convex body from the mean and ...

The problem is considered of maximizing a function in a convex region. To solve this problem a new method is developed, to be called "method of feasible directions". It is a method of steep ascent.

Abstract: Online minimization of an unknown convex function over a convex and compact set is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient ...

This paper presents two different optimization-based trajectory generation methods for multiple aircrafts, i.e., mixed-integer convex programming (MICP) and difference of convex functions (DC) ...

Abstract: It is known that for a strictly concave-convex function, the gradient method introduced by Arrow and Hurwicz [1], has guaranteed global convergence to its saddle point. Nevertheless, there ...

In this paper we show that a log-convex function satisfies Hadamard's inequality, as well as we give an extension for this result in several directions.