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

Nash Equilibria Conditions for Cyclic Games with p Players

Computational network theory : theoretical foundations and applications

The multi-agent optimal control problem involves a decision process with multiple agents, where each agent solves an optimal control problem with the individual cost functional and strategy set, and the cost functional is dependent on all the other agents’ state and/or control variables. Here the “agent” can be understood as a true decision maker, or as an abstract optimization criterion. The strategy sets, along with admissible control set, are often described by a system of parameterized ordinary differential/difference equations (the state dynamic) or partial differential equations, and in realistic settings they may be dependent on the rivals’s variables due to, for example, certain constraints from the common resources. This chapter describes the multi-agent optimal control problem, and studies the reformulation of a system of differential equations constrained by parameterized variational inequalities, along with some initial and/or boundary conditions. This reformulation presents differential equations, variational inequalities, and equilibrium conditions in a systematic way, and is advantageous since it can be treated as a system of differential algebraic equations, for which abundant theory and algorithms are available.

Multi-agent Optimal Control Problems and Variational Inequality Based Reformulations

Mithilfe der am Zentrum fur Angewandte Informatik entwickelten Software TEMPI (Technology Emissions Means Process Identification) steht eine Modellierungsumgebung zur Verfugung, die es ermoglicht, finanzielle Investitionen und ihren Einfluss auf CO 2-Minderungsmassnahmen mithilfe eines zeitdiskreten Modells vergleichend gegenuberzustellen und zu optimieren.

Simulation eines CO 2 -Zertifikatenhandels und algorithmische Optimierung von Investitionen

We consider time discrete systems which are described by a system of difference equations. The related discrete optimal control problems are introduced. Additionally, a gametheoretic extension is derived, which leads to general multicriteria decision problems. The characterization of their optimal behavior is studied. Given starting and final states define the decision process; applying dynamic programming techniques suitable optimal solutions can be gained. We generalize that approach to a special gametheoretic decision procedure on networks. We characterize Nash equilibria and present sufficient conditions for their existence. A constructive algorithm is derived. The sufficient conditions are exploited to get the algorithmic solution. Its complexity analysis is presented and at the end we conclude with an extension to the complementary case of Pareto optima.

Stefan Pickl

Papers

Nash Equilibria Conditions for Cyclic Games with p Players

Computational network theory : theoretical foundations and applications

Multi-agent Optimal Control Problems and Variational Inequality Based Reformulations

Simulation eines CO 2 -Zertifikatenhandels und algorithmische Optimierung von Investitionen

An approach for an algorithmic solution of discrete optimal control problems and their game-theoretical extension