Linear and Convex Optimization: A Mathematical Approach

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Software to accompany book

Chapter 9. Simplex method. This Excel spreadsheet solves linear programs with two or three constraints using the naïve simplex method (algorithm 9.1). The user must choose the entering and leaving variable at each iteration.

Chapter 11. Primal-dual path following algorithm to solve a linear program (algorithm 11.3) This tool runs on the web. It shows the calculations at each iteration. Problems with up to 10 constraints and 10 variables may be entered. 

https://share.streamlit.io/mhveatch/int-point-alg/main/Linear.py

Chapter 15. Primal-dual interior point algorithm to solve convex program Examples 15.9 and 10 from Section 15.4. This tool runs on the web. It shows the equations and calculations at each iteration. 

https://share.streamlit.io/mhveatch/int-point-alg/main/Convex.py

Description
The intended audience is upper level undergraduate mathematics majors, plus business, economics, computer science, and other majors with a linear algebra background. Some features:

• Designed with instructors whose background is mathematics, not operations research, in mind: Clear motivation, mathematical explanations, and organization.
• Thorough instructor’s solutions manual.
• Concise matrix notation is used throughout.
• Mathematical style is used. For example, optimality conditions and duality theory are presented before the simplex method, since they lay the groundwork for it. 
• Thorough numerical examples and motivation are provided.
• No background in algorithms is assumed. Some analysis of algorithms is presented.
• Presents a broad range of applications, many of them recent, to fields like online marketing, disaster response, humanitarian development, public sector planning, health delivery, manufacturing, and supply chain management
• Connections are made between linear, integer, and convex optimization. 
• No software is taught in the book. Most modeling exercises are moderately sized--small enough to readily enter into a solver, e.g., in the LP file format. Algebraic solutions are given to most problems, facilitating translation into any desired modeling language.
• The simplex method is presented first in “naïve” form, then in tableau form. Instructors wishing to start with tableau form can easily do so. The naïve form requires more computation but makes clearer the geometry of the algorithm.