Transcription of Introduction to Semidefinite Programming
{{id}} {{{paragraph}}}
Example: bachelor of science
Introduction to Semidefinite Programming
Introduction to Semidefinite Programming (SDP) Robert M. Freund 1 Introduction Semidefinite Programming (SDP) is the most exc iting development in math ematical Programming in the 1990 s. SDP has applications in such diverse fields as traditional convex constrained optimization, control theory, and combinatorial optimization. Because SDP is solvable vi a interior point methods, most of these applications can usually be solved very efficiently in practice as well as in theory. 2 Revi ew of Linear Programming Consider the linear Programming problem in standard form: LP : minimize c x ai x = bi, i = 1, .. , m n +.x Here x is a vector of n variables, and we write c x for the inner-product P jn =1 cjxj , etc. Also, n + n x 0}, and we call n + the nonnegative orthant. n := {x |In fact, is a closed convex cone, where K is called a closed a convex cone + if K satisfies the following two conditions: 1 P P P3 If x, w K, then x+ w K for all nonnegative scalars and.
X X 4 • If X = QDQT as above, then the columns of Q form a set of n orthogonal eigenvectors of X, whose eigenvalues are the corresponding diagonal entries of D. • X 0 if and only if X = QDQT where the eigenvalues (i.e., the diagonal entries of D) are all nonnegative.
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: