Amitabh Basu is Professor of Applied Mathematics and Statistics at Johns Hopkins University. He has received the NSF CAREER award and the Egon Balas Prize from the INFORMS Optimization Society. He serves on the editorial boards of 'Mathematics of Operations Research,' 'Mathematical Programming,' 'SIAM Journal on Optimization,' and the 'MOS-SIAM Series on Optimization.'

'Written by one of the most brilliant researchers in the field, this book provides an elegant, rigorous and original presentation of the theory of convexity, describing in a unified way its use in continuous and discrete optimization, and also covering some very recent advancements in these areas.' Marco Di Summa, University of Padua

• 1. Preliminaries; Part I. Structural Aspects: 2. Convex sets; 3. Convex functions; 4. Geometry of numbers; Part II. Optimization: 5. Ingredients of mathematical optimization; 6. Complexity of convex optimization with integer variables; 7. Certificates and duality; Hints to selected exercises; References; Index.

Amitabh Basu is Professor of Applied Mathematics and Statistics at Johns Hopkins University. He has received the NSF CAREER award and the Egon Balas Prize from the INFORMS Optimization Society. He serves on the editorial boards of 'Mathematics of Operations Research,' 'Mathematical Programming,' 'SIAM Journal on Optimization,' and the 'MOS-SIAM Series on Optimization.'

'Written by one of the most brilliant researchers in the field, this book provides an elegant, rigorous and original presentation of the theory of convexity, describing in a unified way its use in continuous and discrete optimization, and also covering some very recent advancements in these areas.' Marco Di Summa, University of Padua

• 1. Preliminaries; Part I. Structural Aspects: 2. Convex sets; 3. Convex functions; 4. Geometry of numbers; Part II. Optimization: 5. Ingredients of mathematical optimization; 6. Complexity of convex optimization with integer variables; 7. Certificates and duality; Hints to selected exercises; References; Index.

Amitabh Basu is Professor of Applied Mathematics and Statistics at Johns Hopkins University. He has received the NSF CAREER award and the Egon Balas Prize from the INFORMS Optimization Society. He serves on the editorial boards of 'Mathematics of Operations Research,' 'Mathematical Programming,' 'SIAM Journal on Optimization,' and the 'MOS-SIAM Series on Optimization.'

'Written by one of the most brilliant researchers in the field, this book provides an elegant, rigorous and original presentation of the theory of convexity, describing in a unified way its use in continuous and discrete optimization, and also covering some very recent advancements in these areas.' Marco Di Summa, University of Padua

• 1. Preliminaries; Part I. Structural Aspects: 2. Convex sets; 3. Convex functions; 4. Geometry of numbers; Part II. Optimization: 5. Ingredients of mathematical optimization; 6. Complexity of convex optimization with integer variables; 7. Certificates and duality; Hints to selected exercises; References; Index.