We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Introduction to linear and nonlinear programming

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

http://romisatriawahono.net/lecture/rm/survey/softcomputing/Boussaid%20-%20Optimization%20Metaheuristics%20-%202013.pdf

A survey on optimization metaheuristics

高等学校計算数学学報 = Numerical mathematics

This paper deals with a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno dynamics. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real-world processes do not present the corresponding behavior, mathematical models of some interconnected engineering systems may be Zeno due to the corresponding formal abstraction. We propose a useful approximative approach to Zeno dynamics, namely, a projection based characterization of this phenomena. A resulting trajectory associated with the Zeno dynamics can finally be described as a result of a specific dynamic projection procedure applied to the original model. We use here the projected dynamic systems methodology. The obtained formal description provides an effective theoretic basis for a constructive treatment of the Zeno behaviour. We also discuss an application of the proposed technique to the conventional sliding mode control processes.

Constructive approximations of the Zeno dynamics in affine switched systems: The projection based approach

The fixed point theorem of Kakutani is a generalization of Bouwer’s fixed point theorem which says that every continuous mapping of a convex and compact subset of an n–dimensional Euclidean space into itself has at least one fixed point.

A Dynamical Method for the Calculation of Nash-Equilibria in n–Person Games

This paper studies the dynamic Nash equilibrium problem with shared constraint (NEPSC), a set of optimal control problems with coupled cost functionals and control sets. This problem is reformulated into a variational inequality (VI) posed in an Hilbert space, and a VI-based Galerkin method is proposed for solving its equilibrium solution.

A Galerkin Method for the Dynamic Nash Equilibrium Problem with Shared Constraint

A constructive algorithm for max–min paths problems on energy networks

In Contributions to game theory and management, vol. XI. Collected papers presented on the Eleventh International Conference Game Theory and Management / Editors Leon A. Petrosyan, Nikolay A. Zenkevich. - SPb.: Saint Petersburg State University, 2018. - 330 p. The collection contains papers accepted for the Eleventh International Game Theory and Management (June 28-30, 2017, St. Petersburg State University, St. Petersburg, Russia).

Stefan Pickl

Papers

Constructive approximations of the Zeno dynamics in affine switched systems: The projection based approach

A Dynamical Method for the Calculation of Nash-Equilibria in n–Person Games

A Galerkin Method for the Dynamic Nash Equilibrium Problem with Shared Constraint

A constructive algorithm for max–min paths problems on energy networks

Nash Equilibria in Mixed Stationary Strategies for m-Player Mean Payoff Games on Networks