Linear and Nonlinear Programming with Maple

Linear and Nonlinear Programming with Maple--An Interactive, Applications-Based Approach

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(Note: All worksheets were created using Maple 13.)

Section 1.1: LPSolve Command A basic example illustrating the use of the LPSolve command for solving a linear programming problem.
Section 1.1: LPSolve Matrix Form A convenient way of using the LPSolve command when the LP is expressed in matrix inequality form.
Section 1.2: Solving LPs Graphically Demonstration of how to combine the inequal and contourplot commands for graphically estimating a solution.
Section 2.1: Simplex Algorithm A worksheet for practicing the simplex algorithm.
Section 2.4: Simplex Algorithm as Partitioned Matrix Multiplication Demonstration that each iteration of the simplex algorithm corresponds to multiplication of the original tableau matrix by a partitioned matrix.
Section 2.6: Interior Point Algorithm Implementation of the Projected-Gradient Interior Point Algorithm.
Section 3.1: Diet Problem Solution of the diet problem.
Section 3.2: Transportation Problem A basic transportation model involving three supply points and four demand points.
Section 3.2: Transshipment Problem The preceding transportation model with two transshipment points.
Section 3.3: Minimum Cost Network Flow Problem Worksheet for solving the minimum cost problem, easily modifed to solve the maximum flow problem.
Section 4.2: Sensitivity Analysis Basic sensitivy analysis applied to the FuelPro Problem.
Section 4.3: Dual Simplex Method Example illustrating this alternate means for solving certain LPs.
Section 5.1: Practicing the Branch and Bound Method A worksheet for practicing the branch and bound algorithm using the LPSolve command.
Section 5.1: Solving Mixed Integer Linear Programming Problems Illustration of LPSolve options for solving mixed integer linear programming problems.
Section 5.2: Cutting Plane Algorithm Implementation of this method for solving integer linear programming problems.
Section 6.1: Feasible Regions for NLPs Combination of the piecewise and contour commands for plotting feasible regions corresponding to nonlinear constraints.
Section 6.1: NLP Solve Command A basic example illustrating the use of the NLPSolve command for solving nonlinear programming problem.
Section 6.4: Classifying Critical Points Illustration of how to use the Gradient, Hessian, and Eigenvalues commands to calculate and classify critical points.
Section 7.1: Steepest Descent Method Procedure for estimating minima of a function of two variables using the Steepest Descent Method.
Section 7.2: Newtons Method Newton's Method procedure.
Section 7.3: Levenberg-Marquardt Algorithm Implementation of the Levenberg-Marquardt Algorithm.
Section 8.2: Computing KKT Points Systematic means to compute Karush-Kuhn Tucker (KKT) points, along with corresponding Lagrange multipliers, for constrained optimization problems.
Section 8.4: QPSolve Command Illustration of how to uilize the matrix-input form of the QPSolve command.
Section 8.5: Sequential Quadratic Programming Technique The Sequential Quadratic Programming Technique (SQPT) for solving constrained minimization problems. Easily modified to incorporate merit functions.

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