Sinposis

LINEAR OPTIMIZATION AND DUALIYY: A MODERN EXPOSITION DEPARTS FROM CONVENTION IN SIGNIFICANT WAYS. STANDARD LINEAR PROGRAMMING TEXTBOOKS PRESENT THE MATERIAL IN THE ORDER IN WHICH IT WAS DISCOVERED. DUALITY IS TREATED AS A DIFFICULT ADD-ON AFTER COVERAGE OF FORMULATION, THE SIMPLEX METHOD, AND POLYHEDRAL THEORY. STUDENTS END UP WITHOUT KNOWING DUALITY IN THEIR BONES. THIS TEXT BRINGS IN DUALITY IN CHAPTER 1 AND CARRIES DUALITY ALL THE WAY THROUGH THE EXPOSITION. CHAPTER 1 GIVES A GENERAL DEFINITION OF DUALITY THAT SHOWS THE DUAL ASPECTS OF A MATRIX AS A COLUMN OF ROWS AND A ROW OF COLUMNS. THE PROOF OF WEAK DUALITY IN CHAPTER 2 IS SHOWN VIA THE LAGRANGIAN, WHICH RELIES ON MATRIX DUALITY. THE FIRST THREE LP FORMULATION EXAMPLES IN CHAPTER 3 ARE CLASSIC PRIMAL-DUAL PAIRS INCLUDING THE DIET PROBLEM AND 2-PERSON ZERO SUM GAMES. FOR MANY ENGINEERING STUDENTS, OPTIMIZATION IS THEIR FIRST IMMERSION IN RIGOROUS MATHEMATICS. CONVENTIONAL TEXTS ASSUME A LEVEL OF MATHEMATICAL SOPHISTICATION THEY DON'T HAVE. THIS TEXT EMBEDS DOZENS OF READING TIPS AND HUNDREDS OF ANSWERED QUESTIONS TO GUIDE SUCH STUDENTS.