Updated:
My list of reference materials containing for mathematical optimisation, based on Quora.
Lecture notes
Highly recommended: video lectures by Prof. S. Boyd at Stanford, this is a rare case where watching live lectures is better than reading a book.

EE263: Introduction to Linear Dynamical Systems (video): http://www.stanford.edu/~boyd/ee263/videos.html

EE363: Linear Dynamical Systems: http://www.stanford.edu/class/ee363/

EE364a: Convex Optimization I (video): http://www.stanford.edu/class/ee364a/videos.html

EE364b: Convex Optimization II (video): http://www.stanford.edu/class/ee364b/videos.html

6.253: Convex analysis and optimization: http://ocw.mit.edu/courses/electricalengineeringandcomputerscience/6253convexanalysisandoptimizationspring2010/lecturenotes/

Optimization courses at MIT: http://optimization.mit.edu/classes.php

Optimisation Course in CMU 10725 Optimization Fall 2012
Books

S. Bubeck, “Convex Optimization: Algorithms and Complexity”, arXiv:1405.4980, 2015

F. Clarke, “Functional Analysis, Calculus of Variations and Optimal Control”, Springer, 2013

Liberzon, D., “Calculus of Variations and Optimal Control Theory  A Concise Introduction”, Princeton University Press, 2012

S. Boyd and L. Vandenberghe, “Convex Optimization”, Cambridge University Press, 2004

G. Calafiore and L. El Ghaoui, “Optimization Models”, Cambridge University Press, 2014

R. T. Rockarfellar and R. J. B. Wets, “Variational Analysis”, Springer, 1998

D. G. Luenberger and Y. Ye, “Linear and Nonlinear Programming”, 4th ed., Springer, 2016

J. Frédéric Bonnans, J. Charles Gilbert, C. Lemaréchal and C. A. Sagastizábal, “Numerical Optimization”, 2nd ed., Springer, 2006

Papadimitriou & Steiglitz, Combinatorial Optimization: Algorithms and Complexity: http://www.amazon.com/CombinatorialOptimizationAlgorithmsChristosPapadimitriou/dp/0486402584

Lawson & Hanson, Solving Least Squares Problems: http://books.google.com/books/about/Solving_Least_Squares_Problems.html?id=ROw4hU85nz8C

Bellman, Dynamic Programming: http://www.amazon.com/DynamicProgrammingRichardBellman/dp/0486428095/

Bellman, Applied Dynamic Programming: http://www.amazon.com/AppliedDynamicProgrammingRichardBellman/dp/B0000CLNVK

Bellman, Adaptive Control Processes: http://www.amazon.com/AdaptiveControlProcessesBellman/dp/0691079013

Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning: http://www.amazon.com/GeneticAlgorithmsOptimizationMachineLearning/dp/0201157675
 Gill, Murray, Wright, Practical Optimization: http://www.amazon.com/PracticalOptimizationPhilipGill/dp/0122839528

BenTal & Nemirovsky, Lectures on Modern Convex Optimization: http://www.amazon.com/LecturesModernConvexOptimizationApplications/dp/0898714915

Bertsekas, Introduction to Linear Optimization: http://www.amazon.com/IntroductionLinearOptimizationScientificComputation/dp/1886529191

Bertsekas, Convex Analysis and Optimization: http://www.amazon.com/ConvexAnalysisOptimizationDimitriBertsekas/dp/1886529450

Bertsekas, Nonlinear programming: http://www.amazon.com/NonlinearProgrammingDimitriPBertsekas/dp/1886529000/

Bertsekas, Dynamic Programming and Optimal Control: http://www.amazon.com/DynamicProgrammingOptimalControlVol/dp/1886529086

Rockafellar, Convex Analysis: http://www.amazon.com/AnalysisPrincetonLandmarksMathematicsPhysics/dp/0691015864/

Nesterov, Introductory Lectures on Convex Optimization: A Basic Course: http://www.amazon.com/IntroductoryLecturesConvexOptimizationApplied/dp/1402075537

Ruszczynski, Nonlinear Optimization: http://www.amazon.com/NonlinearOptimizationAndrzejRuszczynski/dp/0691119155/

Fletcher, Practical Methods of Optimization: http://www.amazon.com/PracticalMethodsOptimizationRFletcher/dp/0471494631

Nocedal & Wright, Numerical Optimization: http://www.amazon.com/NumericalOptimizationOperationsFinancialEngineering/dp/0387303030/ Press et al.

Numerical Recipes: http://www.amazon.com/NumericalRecipes3rdScientificComputing/dp/0521880688

Dennis & Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations: http://www.amazon.com/NumericalUnconstrainedOptimizationNonlinearMathematics/dp/0898713641

Cornuejols & Tütüncü, Optimization Methods in Finance: http://www.amazon.com/OptimizationMethodsFinanceMathematicsRisk/dp/0521861705/

Stengel, Optimal Control and Estimation: http://www.amazon.com/OptimalControlEstimationAdvancedMathematics/dp/0486682005/

Kirk, Optimal Control Theory: http://www.amazon.com/OptimalControlTheoryDonaldKirk/dp/0486434842/

Spall, Introduction to Stochastic Search and Optimization: http://www.amazon.com/IntroductionStochasticSearchOptimizationJames/dp/0471330523/

Lasdon, Optimization Theory for Large Systems: http://www.amazon.com/OptimizationTheoryLargeSystemsLasdon/dp/0486419991

Deb & Kalyanmoy, MultiObjective Optimization Using Evolutionary Algorithms: http://www.amazon.com/MultiObjectiveOptimizationUsingEvolutionaryAlgorithms/dp/047187339X

Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning: http://www.amazon.com/GeneticAlgorithmsOptimizationMachineLearning/dp/0201157675/

Minoux, Mathematical Programming: http://www.amazon.com/MathematicalProgrammingWileyIntersciencemathematicsoptimization/dp/0471901709

Camacho & Alba: Model Predictive Control: http://www.amazon.com/PredictiveControlAdvancedTextbooksProcessing/dp/1852336943

Hillier, Introduction to Operations Research: http://www.amazon.com/IntroductionOperationsResearchStudentAccess/dp/0077298349/

Puterman, Markov Decision Processes: http://www.amazon.com/MarkovDecisionProcessesProgrammingProbability/dp/0471727822
 Powell, Approximate Dynamic Programming: http://www.amazon.com/ApproximateDynamicProgrammingDimensionalityProbability/dp/0470171553/
Other

Grešovnik, Optimization Links: http://www2.arnes.si/~ljc3m2/igor/links.html

8 Arsham, Intro to Modeling and Optimization: http://home.ubalt.edu/ntsbarsh/opre640a/partviii.htm

Matlab Optimization Toolbox resources: http://www.mathworks.com/help/toolbox/optim/

Bennett et al., The Interplay of Optimization and Machine Learning Research: http://jmlr.csail.mit.edu/papers/volume7/MLOPTintro06a/MLOPTintro06a.pdf

Evolutionary algorithms chapter in Jason Brownlee’s book : http://www.cleveralgorithms.com/natureinspired/evolution.html

Brent, Algorithms for Minimization without Derivatives: http://mathspeople.anu.edu.au/~brent/pub/pub011.html
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