Optimization Models
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1. Introduction
1.1. Overview
1.2. Optimization Models
2. Linear Algebra
2.1. Vectors
2.2. Matrices
2.3. Linear Equations
2.4.  Least-Squares
2.5. Eigenvalues
2.6  Singular Values
3. Convex Models
3.1. Convexity
3.2. LP and QP
3.3. SOCP
3.4. Robust LP
3.5. GP
3.6. SDP
3.7. Non-Convex Models
4. Duality
4.1. Weak Duality
4.2. Strong Duality
4.3.  Applications
5. Case Studies
5.1. Senate Voting
5.2. Antenna Arrays
5.3. Localization
5.4. Circuit Design

Exercises

  1. We seek to optimize the shape of a box-shaped structure with height h, width w, and depth d. Due to cost concerns, we have an upper limit A_{rm wall} on the total wall area 2(hw + hd), another upper limit A_{rm floor} on the floor area wd. For structural reasons, we have lower and upper bounds alpha,beta on the aspect ratio h/w, and similar bounds gamma,delta on the aspect ratio w/d. Subject to these constraints, we wish to maximize the volume of the structure, hwd.

    1. Express the problem in the standard form for an optimization problem.

    2. Express this problem as a geometric program (GP) in standard GP form. (Note: you are not asked to put it in the standard convex form for GPs.)