Lect01

Lect01 - D. Bertsekas EE553 LECTURE 1 LECTURE OUTLINE...

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EE553 LECTURE 1 LECTURE OUTLINE Nonlinear Programming Application Contexts Characterization Issue Computation Issue Duality Organization D. Bertsekas Adapted for USC EE553 by M. Safonov © D. Bertsekas, MIT, Cambridge, MA
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NONLINEAR PROGRAMMING min x X f ( x ) , where f : ± n ²→± is a continuous (and usually differ- entiable) function of n variables X = ± n or X is a subset of ± n with a “continu- ous” character. If X = ± n , the problem is called unconstrained If f is linear and X is polyhedral, the problem is a linear programming problem. Otherwise it is a nonlinear programming problem Linear and nonlinear programming have tradi- tionally been treated separately. Their method- ologies have gradually come closer. Adapted for USC EE553 by M. Safonov © D. Bertsekas, MIT, Cambridge, MA
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TWO MAIN ISSUES Characterization of minima Necessary conditions Sufficient conditions Lagrange multiplier theory Sensitivity Duality Computation by iterative algorithms Iterative descent Approximation methods Dual and primal-dual methods Adapted for USC EE553 by M. Safonov © D. Bertsekas, MIT, Cambridge, MA
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Lect01 - D. Bertsekas EE553 LECTURE 1 LECTURE OUTLINE...

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