Lecture 8 : Strong Duality

نویسنده

  • Laurent El Ghaoui
چکیده

In this section, we consider a convex optimization problem p * := min x f 0 are affine. We denote by D the domain of the problem (which is the intersection of the domains of all the functions involved), and by X ⊆ D its feasible set.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Ee 381v: Large Scale Optimization 12.1 Last Time 12.2 Quadratically Constrained Quadratic Program

In the previous lecture, in the first place, we talked about duality for general non-convex optimization. And we know that dual functions are always convex. The dual of the dual problem is also convex. In applications, the dual of the dual can be used as the convex relaxation of the primal (and we will see this explicitly in the next lecture). Then, we covered the concepts of weak duality and s...

متن کامل

Lecture 16 : Duality and the Minimax theorem

Last lecture we introduce linear programs (LP) and saw how to model problems with LPs. In this lecture we study duality of LPs. Roughly speaking, the dual of a minimization LP is a maximization LP which its solutions provide lower bounds for the optimum of the original LP. First we show how to construct dual of an LP. Then we talk about relation between the optimum of an LP and its dual. In par...

متن کامل

Lecture 16: Strong duality

In the last lecture we saw how to formulate a dual program for an optimization problem. From the formulation, it turned out that the dual program gave an upper/lower bound depending on whether the problem was maximization/minimization respectively. Today, the focus will be on when are these bounds tight. It turns out that these bounds are tight in most of the cases of interest like linear progr...

متن کامل

Dualities in Supersymmetric Field Theories

These lectures briefly introduce dualities in four-dimensional quantum field theory, and summarize results found in supersymmetric field theories. The first lecture describes physical aspects of electric-magnetic (EM), strong-weak coupling (S), and infrared (IR) dualities. The second lecture focuses on results and conjectures concerning S-duality in N=2 supersymmetric gauge theories. The third ...

متن کامل

Lecture notes 5: Duality in applications

We have already seen how to take the dual of a linear program in general form. However, when we are solving a problem using linear programming, it can be very enlightening to take the dual of the linear program for that particular problem. Typically, in the context of the problem under study, it is possible to give a natural interpretation to the dual variables, and this also often leads to nat...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012