This paper proposes and analyzes an accelerated inexact dampened augmented Lagrangian (AIDAL) method for solving linearly-constrained nonconvex composite optimization problems. Each iteration of the AIDAL consists of: (i) inexactly a proximal (AL) subproblem by calling gradient (ACG) subroutine; (ii) applying under-relaxed Lagrange multiplier update; (iii) using novel test to check whether pena...

We consider the linearly constrained `1-`2 minimization and propose the accelerated Bregman method for solving this minimization problem. The proposed method is based on the extrapolation technique, which is used in accelerated proximal gradient methods studied by Nesterov, Nemirovski, and others, and the equivalence between the Bregman method and the augmented Lagrangian method. O( 1 k2 ) conv...

BACKGROUND AND AIMS Plants are expected to maximize their net photosynthetic gains and efficiently use available resources, but the fundamental principles governing trade-offs in suites of traits related to resource-use optimization remain uncertain. This study investigated whether Acer saccharum (sugar maple) saplings could maximize their net photosynthetic gains through a combination of crown...

We give a nonstandard variant of Jordan’s proof of the Jordan curve theorem which is free of the defects his contemporaries criticized and avoids the epsilontic burden of the classical proof. The proof is selfcontained, except for the Jordan theorem for polygons taken for granted.

In the field of global optimization many efforts have been devoted to solve unconstrained global optimization problems. The aim of this paper is to show that unconstrained global optimization methods can be used also for solving constrained optimization problems, by resorting to an exact penalty approach. In particular, we make use of a nondifferentiable exact penalty function Pq(x; ε). We show...

We consider constrained partial differential equations of hyperbolic type with a small parameter ε>0, which turn parabolic in the limit case, i.e., for ε=0. The well-posedness resulting systems is discussed and corresponding solutions are compared terms ε. For analysis, we system as differential–algebraic equation based on variational formulation problem. particular choice initial data, reach f...