Chair of Applied Mechanics

Optimization for engineers

Short description

The basics of optimization are presented, with a focus on common and proven optimization methods for problems in the field of applied structural optimization.

An introduction provides basic knowledge of mathematical concepts and aspects of optimization. Afterwards, optimization problems without restrictions and problems with restrictions are considered. Based on this, alternative formulations of an optimization problem (so-called Lagrange duality) are presented with the help of Lagrange functions. Subsequently, approximation procedures, optimality criteria procedures and multi-criteria optimization are considered. Finally, perspectives on further areas such as shape optimization and topology optimization are given.


  • Introductio 
    • Introduction and motivation
    • Basic concepts and general form of the optimization problem
    • Some mathematical terms and properties
  •   Optimization without restrictions
    • optimality criteria
    • One-dimensional optimization / line search / incomplete line search
    • Multidimensional optimization
  • Optimization with restrictions
    • optimality criteria
    • Lagrange function, saddle point, duality
    • Indirect methods
    • Direct methods
    • approximation method
    • Evolutionary methods and genetic algorithms
    • Concluding remarks and practical tips


  • Basic knowledge in engineering mechanics and advanced mathematics


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