Matrix Multiplicative Weight Updates for Solving SDPs
نویسنده
چکیده
In this write-up, we elucidate an algorithm based on matrix multiplicative weight updates to near-optimally solve SDPs.
منابع مشابه
Parallelized Solution to Semidefinite Programmings in Quantum Complexity Theory
In this paper we present an equilibrium value based framework for solving SDPs via the multiplicative weight update method which is different from the one in Kale’s thesis [Kal07]. One of the main advantages of the new framework is that we can guarantee the convertibility from approximate to exact feasibility in a much more general class of SDPs than previous result. Another advantage is the de...
متن کاملSolving LPs/SDPs via Multiplicative Weighs
From the previous lecture, we have proved the following lemma. Lemma 1. If the cost vector c t ∈ [−ρ, ρ] n , and T ≥ 4ρ 2 ln n 2 , then average loss 1 T T t=1 p t c t ≤ 1 T T t=1 c t (i) + , ∀i ∈ [n] In this lecture, we are going to see the application of multi-weight algorithm for solving LPs and SDPs. For illustration purpose, we will be working on an LP example (the LP relaxation for set cov...
متن کاملEfficient Multiplicative Updates for Support Vector Machines
The dual formulation of the support vector machine (SVM) objective function is an instance of a nonnegative quadratic programming problem. We reformulate the SVM objective function as a matrix factorization problem which establishes a connection with the regularized nonnegative matrix factorization (NMF) problem. This allows us to derive a novel multiplicative algorithm for solving hard and sof...
متن کاملweight updates : LP solving , Portfolio Management
Today we see how to use the multiplicative weight update method to solve other problems. In many settings there is a natural way to make local improvements that ”make sense.” The multiplicative weight updates analysis from last time (via a simple potential function) allows us to understand and analyse the net effect of such sensible improvements. (Formally, what we are doing in many settings is...
متن کاملMultiplicative updates For Non-Negative Kernel SVM
We present multiplicative updates for solving hard and soft margin support vector machines (SVM) with non-negative kernels. They follow as a natural extension of the updates for non-negative matrix factorization. No additional parameter setting, such as choosing learning, rate is required. Experiments demonstrate rapid convergence to good classifiers. We analyze the rates of asymptotic converge...
متن کامل