## Non-linear optimization theory applied to floor plan design |

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### Contents

FORMULATION AS A NONLINEAR PROGRAMMING PROBLEM | 6 |

DESCRIPTION OF NONLIN | 12 |

METHODS OF DEALING WITH THE NONCONVEX CONSTRAINTS | 16 |

2 other sections not shown

### Common terms and phrases

algorithm APPROXIMATIONS FOR AREA BED3 BftTH budget constraint COMPARISON OF SOLUTIONS construction cost descent direction dimension and shape dimensioning problem dimensioning variables DIMENSIONLESS REPRESENTATION dlmensionless endpoints EQUAL OBJECTIVE feasible region feasible solutions FIGURE 17 Figure 21 Figure IB finite number floor plan layouts global optimum grid initial point INTERSECTING AND TANGENT j=MINX(i KITCHEN 6.0 LBPR(i length and width length of room LINEAR AND NON-LINEAR linear area approximation linear constraints linear programming lower area bounds lower bound lower width MAXX(i non-convex constraints NON-LINEAR AREA CONSTRAINTS non-linear programming problem NONLIN number of iterations objective function OPTIMAL SOLUTION Optimization Theory original problem quadratic approximation rate of convergence relaxed mode RESULTS FOR DISSECTION room arrangement running in relaxed SAMPLE PROBLEM 44 shape requirements SOLUTION FOR DISSECTION SOLUTION WITH BUDGET SOLUTIONS USING LINEAR solve tangent line test runs thesis topologically feasible UNIVERSITY OF CALIFORNIA upper area bounds upper bound upper width width of room