suc凸优化2020春季学期cvxdcp_note.pdfVIP

Constructive Convex Analysis and Disciplined Convex Programming Stephen Boyd and Steven Diamond and Jaehyun Park EE CS Departments Stanford University SIST, Shanghai, March 26-28 2016 1 Outline Convex Optimization Constructive Convex Analysis Disciplined Convex Programming Modeling Frameworks Conclusions 2 Outline Convex Optimization Constructive Convex Analysis Disciplined Convex Programming Modeling Frameworks Conclusions Convex Optimization 3 Convex optimization problem — standard form minimize f (x ) 0 subject to fi (x ) Æ 0, i = 1, . . . , m Ax = b with variable x œ Rn I objective and inequality constraints f , . . . , f are convex 0 m for all x , y , ◊ œ [0, 1], f (◊x + (1 ≠ ◊)y ) Æ ◊ f (x ) + (1 ≠ ◊)f (y ) i i i i.e., graphs of fi curve upward I equality constraints are linear Convex Optimization 4 Convex optimization problem — conic form cone program: T minimize c x subject to Ax = b, x œ K with variable x œ Rn I linear objective, equality constraints; K is convex cone I special cases: I linear program (LP) I semidefinite program (SDP) I the modern canonica