Author | Razumikhin, B. S. author |
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Title | Physical Models and Equilibrium Methods in Programming and Economics [electronic resource] / by B. S. Razumikhin |
Imprint | Dordrecht : Springer Netherlands, 1984 |
Connect to | http://dx.doi.org/10.1007/978-94-009-6274-3 |
Descript | XV, 351 p. online resource |
I: Equilibrium of mechanical systems with linear constraints and linear programming problems -- 1.1. Introduction -- 1.2. Linear equations and inequalities -- 1.3. Systems of linear equations and inequalities -- 1.4. Linear programming problems. Duality theorems -- II: Equilibrium of physical systems and linear programming problems -- 2.1. Introduction -- 2.2. Some concepts from thermodynamics -- 2.3. Physical models of dual pairs of systems of linear equations and inequalities. Alternative theorems -- 2.4. A physical model for linear programming problems. Equilibrium conditions -- 2.5. Penalty methods -- 2.6. Some properties of approximate solutions of dual problems of linear programming problems -- 2.7. Models for transport type problems -- III: The method of redundant constraints and iterative algorithms -- 3.1. Introduction -- 3.2. The method of redundant constraints -- 3.3. The first iterative algorithm for solving linear programming problems and for solving systems of linear equations and inequalities -- 3.4. The second algorithm -- 3.5. Reduction of the general linear programming problem to a sequence of inconsistent systems. The third algorithm -- IV: The principle of removing constraints -- 4.1. Introduction -- 4.2. The method of generalized coordinates -- 4.3. The method of multipliers -- 4.4. Elastic constraints. Penalty function methods -- 4.5. Discussion -- V: The hodograph method -- 5.1. Introduction -- 5.2. The hodograph method for linear programming problems -- 5.3. Solution of the dual problem -- 5.4. Results of numerical experiments -- VI: The method of displacement of elastic constraints -- 6.1. Introduction -- 6.2. The first algorithm -- 6.3 The second algorithm -- 6.4. Combining the algorithms -- VII: Decomposition methods for linear programming problems -- 7.1. Introduction -- 7.2. Decomposition algorithms -- 7.3. Allocation of resources problems -- VIII: Nonlinear programming -- 8.1. Introduction -- 8.2. The principle of virtual displacements and the Kuhn-Tucker theorem -- 8.3. Numerical methods for solving nonlinear programming problems -- IX: The tangent method -- 9.1. Introduction -- 9.2. Constrained minimization problems -- 9.3. Linear programming -- 9.4. Dynamic problems of optimal control -- X: Models for economic equilibrium -- 10.1. Introduction -- 10.2. Equilibrium problems for linear exchange models -- 10.3. An algorithm for solving numerically equilibrium problems for linear exchange economies -- 10.4. Discussion. The Boltzmann principle -- 10.5. Equilibrium of linear economic models -- 10.6 Physical models for economic equilibrium. The equilibrium theorem -- 10.7. An algorithm for solving equilibrium problems for linear economic models -- 10.8. A generalization of the economic equilibrium problem -- XI: Dynamic economic models -- 11.1. Introduction -- 11.2. The Von Neumann-Gale model. Growth rates and interest rates -- 11.3. A method for solving the problem of maximum growth rates -- 11.4. Duality and problems of growth rates and interest rates -- 11.5. The minimal time problem -- 11.6. A time optimal control problem economic growth -- 11.7. A physical model for solving optimal control problems -- 11.8. Decomposition for time optimal control problems -- 11.9. Optimal balanced growth problems -- XII: Optimal control problems