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Aim of the optimization process is identifying the conditions giving the maximum or minimum value of a function. In system level optimization, objective function is the function of multiple variables. It is very common in engineering Problems, that there are multiple objective functions to be minimized simultaneously, that require special optimization methods.In optimization of a structure, if the structure is subject to simultaneous multiple load cases, combinations of load cases should be considered and worst possible load case should be investigated. However, implementation of conventional optimization approaches into these optimization problems may be impractical due to excessive Central Processing Unit (CPU) times since consideration of multiple load cases increases the associated computational load. In this book, optimization methods along with their applications, structural reanalysis and design sensitivity reanalysis in structural optimization are revisited. In addition, application and advantages of Singular Value Decomposition (SVD) to structural design optimization and Sherman-Morrison-Woodbury (SMW) formulas are investigated.