The data-flow of a numerical program is reversed in its adjoint. We discuss the combinatorial optimization problem that aims to find optimal checkpointing schemes at the level of call trees. For a given amount of persistent memory the objective is to store selected arguments and/or results of subroutine calls such that the overall computational effort (the total number of floating-point operati...

This means we cannot justify the correctness of the “Partition” subroutine by the Hoare’s axiom on program verification. This article is organized as follows. First, we present several fundamental properties of “while” program and finite sequence. Second, we define the “Partition” subroutine on SCMPDS, the task of which is to split a sequence into a smaller and a larger subsequence. The definit...

This means we cannot justify the correctness of the “Partition” subroutine by the Hoare’s axiom on program verification. This article is organized as follows. First, we present several fundamental properties of “while” program and finite sequence. Second, we define the “Partition” subroutine on SCMPDS, the task of which is to split a sequence into a smaller and a larger subsequence. The definit...

The Algorithm2 for a n-link manipulator movement amidst arbitrary unknown static obstacles for a case when a sensor system supplies information about local neighborhoods of different points in the configuration space is presented. The Algorithm2 guarantees the reaching of a target position in a finite number of steps. The Algorithm2 is reduced to a finite number of calls of a subroutine for pla...

An exact algorithm for a n-link manipulator movement amidst arbitrary unknown static obstacles is presented. The algorithm guarantees the reaching of a target configuration of the manipulator in a finite number of steps. The algorithm is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm...

For convex minimization we introduce an algorithm based on VU-space decomposition. The method uses a bundle subroutine to generate a sequence of approximate proximal points. When a primal-dual track leading to a solution and zero subgradient pair exists, these points approximate the primal track points and give the algorithm’s V, or corrector, steps. The subroutine also approximates dual track ...