Learn · Variational Methods in Mechanics

Lecture 12 of 44Summary of finite-variable optimization

Lec12-Part II - Sufficient conditions for constrained minimization

Prof. Ananthasuresh and Prof. Safvan Palathingal · IISc Bangalore

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Variational Methods in Mechanics, IISc Bangalore (at NPTEL)
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All the lectures

  1. Lec1-Part I-Classification of optimization problems and the place of Calculus of Variations in it Video
  2. Lec2-Part II-Classification of optimization problems and the place of Calculus of Variations in it Video
  3. Lec3-Part I - Genesis of Calculus of Variations Video
  4. Lec4-Part II - Genesis of Calculus of Variations Video
  5. Lec5-Part I - Formulation of Calculus of Variations problems in geometry and mechanics and design Video
  6. Lec6-Part II - Formulation of Calculus of Variations problems in geometry and mechanics and design Video
  7. Lec7-Part I - Unconstrained minimization in one and many variables Video
  8. Lec8-Part II - Unconstrained minimization in one and many variables Video
  9. Lec9-Part I - Constrained minimization KKT conditions Video
  10. Lec10-Part II - Constrained minimization KKT conditions Video
  11. Lec11-Part I - Sufficient conditions for constrained minimization Video
  12. Lec12-Part II - Sufficient conditions for constrained minimization Video
  13. Lec13-Part I-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spaces Video
  14. Lec14-Part II-Mathematical preliminaries function, functional, metrics and metric space, norm and vector spaces Video
  15. Lec15-Function spaces and Gateaux variation Video
  16. Lec16-First variation of a functional Freche?t differential and variational derivative Video
  17. Lec17-Part I-Fundamental lemma of calculus of variations and Euler Lagrange equations Video
  18. Lec18-Part II-Fundamental lemma of calculus of variations and Euler Lagrange equations Video
  19. Lec19-Extension of Euler-Lagrange equations to multiple derivatives Video
  20. Lec20-Extension of Euler-Lagrange equations to multiple functions in a functional Video
  21. Lec 21-Part I-Global Constraints in calculus of variations Video
  22. Lec22-Part II-Global Constraints in calculus of variations Video
  23. Lec23-Part I-Local (finite subsidiary) constrains in calculus of variations Video
  24. Lec 24-Part II-Local (finite subsidiary) constrains in calculus of variations Video
  25. Lec25-Part I-Size optimization of a bar for maximum stiffness for given volume Video
  26. Lec26-Part II-Size optimization of a bar for maximum stiffness for given volume Video
  27. Lec27-Part III-Size optimization of a bar for maximum stiffness for given volume Video
  28. Lec28-Part I-Calculus of variations in functionals involving two and three independent variables Video
  29. Lec29-Part II-Calculus of variations in functionals involving two and three independent variables Video
  30. Lec30-Part I-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditions Video
  31. Lec31-Part II-General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditions Video
  32. Lec32-Variational (energy) methods in statics; principles of minimum potential energy and virtual work Video
  33. Lec33-Part I-General framework of optimal structural designs Video
  34. Lec34-Part II-General framework of optimal structural designs Video
  35. Lec35-Optimal structural design of bars and beams using the optimality criteria method Video
  36. Lec36-Invariants of Euler-Lagrange equations and canonical forms Video
  37. Lec37-Noether’s theorem Video
  38. Lec38-Minimum characterization of Sturm-Liouville problems Video
  39. Lec39-Rayleigh quotient for natural frequencies and mode shapes of elastic systems Video
  40. Lec40-Stability analysis and buckling using calculus of variations Video
  41. Lec41-Strongest (most stable) column Video
  42. Lec42-Dynamic compliance optimization Video
  43. Lec43-Electro-thermal-elastic structural optimization Video
  44. Lec44-Formulating the extremization problem starting from the differential equation, self-adjointness of the differential operator, and methods to deal with conservative and dissipative system Video