Lots of background material (eg, on linear algebra) can be found on the ‘‘Livebook’’ on optimization. (You will need to register; it is free.)
This book, by Calafiore and El Ghaoui, provides an introduction to optimization and linear algebra as well.
Convex Optimization, by S. Boyd and L. Vandenberghe.
Linear and nonlinear programming by D. Luenberger.
Nonlinear programming by D. Bertsekas.
Robust optimization by A. Bental, L. El Ghaoui, A. Nemirovski.
Lectures on Convex Optimization, by A. Juditsky.
Introductory lectures on convex optimisation, by Y. Nesterov.
Convex Analysis, by R.T. Rockafellar.
Numerical optimization, by J. Nocedal & S. Wright.
Lectures on modern convex optimization, by A. Nemirovski.
Optimization for Machine Learning, by S. Sra, S. Nowozin, S. Wright.