Suchergebnisse

AbstractStochastic integer programming is a suitable tool for modeling hierarchical decision situations with combinatorial features. In continuation of our work on the design and analysis of heuristics for such problems, we now try to find optimal solutions. Dynamic programming techniques can be used to exploit the structure of two–stage scheduling, bin packing and multiknapsack problems. Numerical results for small instances of these problems are presented.

[EN] The linear programming (LP) approach to solve the Bellman equation in dynamic programming is a well-known option for finite state and input spaces to obtain an exact solution. However, with function approximation or continuous state spaces, refinements are necessary. This paper presents a methodology to make approximate dynamic programming via LP work in practical control applications with continuous state and input spaces. There are some guidelines on data and regressor choices needed to obtain meaningful and well-conditioned value function estimates. The work discusses the introduction of terminal ingredients and computation of lower and upper bounds of the value function. An experimental inverted-pendulum application will be used to illustrate the proposal and carry out a suitable comparative analysis with alternative options in the literature. ; The authors are grateful for the financial support of the Spanish Ministry of Economy and the European Union, grant DPI2016-81002-R (AEI/FEDER, UE), and the PhD grant from the Government of Ecuador (SENESCYT). ; Diaz, H.; Sala, A.; Armesto Ángel, L. (2020). A linear programming methodology for approximate dynamic programming. International Journal of Applied Mathematics and Computer Science (Online). 30(2):363-375. https://doi.org/10.34768/amcs-2020-0028 ; S ; 363 ; 375 ; 30 ; 2

SummaryThis report presents an approach to stochastic programming. It treats mainly the difficulties arising in formulating the problem and the possibilities to derive a deterministic problem by which it can be replaced. In a sense the approach of this report unifies different viewpoints on stochastic programming problems as they have been published in the literature.

AbstractApplicative programming notations offer important advantages over conventional ones both for software development and for the full exploitation of multiprocessor computer systems. They simplify the software developer's tools and techniques, streamline his picture of the equipment on which his software will run, and provide him with powerful modularization facilities for coping with the complexity of application problems. Their simple and mathematically sound semantics support formal reasoning about programs and proofs of their correctness, and the absence of explicit sequencing in applicative programs facilitates their execution by systems of multiple concurrent processors.A familiar—if limited—example of applicative programming is the ubiquitous dynamic spreadsheet. The commercial success of spreadsheet packages demonstrates the appeal of abstractness, and an examination of spreadsheets' "formula" facilities reveals why applicative programming and concurrent processing go so well together.The primary obstacles to widespread adoption of applicative programming are the scarcity of efficient implementations and the novelty and immaturity of the software technology. Applicative programming's fundamental soundness and the leverage it offers in coping with two of contemporary computing's most urgent problems argue that in time these obstacles will be overcome.

One: Convex Sets -- 1. Convex hulls, polytopes and vertices -- 2. Basic solutions of equations -- 3. Theorem of the separating hyperplane -- 4. Alternative solutions of linear inequalities 10 Exercises -- Two: The Theory of Linear Programming -- 1. Examples and classes of linear programmes -- 2. Fundamental duality theorem -- 3. Equilibrium theorems -- 4. Basic optimal vectors -- 5. Graphical method of solution -- Exercises -- Three: The Transportation Problem -- 1. Formulation of problem and dual -- 2. Theorems concerning optimal solutions -- 3. Method of solution with modifications for degeneracy -- 4. Other problems of transportation type -- Exercises -- Four: The Simplex Method -- 1. Preliminary discussion and rules -- 2. Theory of the simplex method -- 3. Further techniques and extensions -- Exercises -- Five: Game Theory -- 1. Two-person zero-sum games -- 2. Solution of games: saddle points -- 3. Solution of games: mixed strategies -- 4. Dominated and essential strategies -- 5. Minimax theorem -- 6. Solution of matrix games by simplex method -- Exercises -- Suggestions for Further Reading -- Solutions to Exercises.

Table of Contents -- Introduction -- Basic Components -- Simple Output and Input -- C's Built-In Functions -- Standard Libraries -- Some Tips for C -- In Depth C Ideas -- Memory Management -- Networking in Unix -- FAQ's -- Macro Conventions -- Code Library