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The availability of cheap, powerful computers, together with the promise of artificial intelligence has drawn the attention of engineering designers, operations analysts, applied mathematicians, and economists to the subject of modeling--the mathematical description of a physical or economic system. A natural purpose of modeling is optimization: finding the best value for some goal associated with the model. This is a textbook about modeling, in particular about modeling for design optimization and the mutual interaction between these two processes. It presents a condensed version of classical optimization theory and numerical algorithms, which it integrates with the newer ideas of monotonicity analysis and model boundedness. Careful definition of new concepts and rigorous proof of simple but important principles are followed by immediate applications.

Mathematical models --- Mathematical optimization --- Mathematical optimization. --- Mathematical models. --- Models, Mathematical --- Simulation methods --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- System analysis --- 21030 --- engineering --- p1030 --- design --- optimisation --- 20020 --- ... --- 31030 --- mathematical models --- 10520 --- mathematical models of optimisation in engineering design --- s0030 --- applications --- of --- in --- computer system --- Optimisation mathématique --- Optimisation mathématique --- Conception --- Modélisation