Semidefinite and Second Order Cone Programming Seminar Fall 2012
نویسندگان
چکیده
The dissertation by Maryam Fazel, “Matrix Rank Minimization with applications”, [3], focuses on minimizing ranks over matrices of convex sets which is genrally an NP-hard problem. The work provides a new heuristics for solving Rank Minimization Problem (RMP) for PSD matrices, which contrary to hitherto developed heuristics, do not require an initial point, are numerically efficient and provide a global lower bound on the optimal value. In addition it also provides a way of embedding a general RMP in a larger PSD problem.
منابع مشابه
Semidefinite and Second Order Cone Programming Seminar Fall 2012 Lecture 2
1 Overview We had a general overview of semidefinite programming(SDP) in lecture 1, starting from this lecture we will be jumping into the theory. Some topics we will discuss in the next few lectures include: the duality theory, notion of complementary slackness, at least one polynomial time algorithm of solving SDP and application in integer programming and combinatorial optimization. Througho...
متن کاملSemidefinite and Second Order Cone Programming Seminar Fall 2012 Project Report Shape Constraints And Its Application
In this project, I will introduce a method to estimate the function by cubic splines. As an example, I will focus on the non-homogeneous Poisson process. Since this method uses an optimization model based on the maximum likelihood principle, it may applied to other stochastic processes. The most critical point of this presentation is a nonnegativity constriant on the splines. In addition, choos...
متن کاملSemidefinite and Second Order Cone Programming Seminar Fall 2012 Project: Robust Optimization and its Application of Robust Portfolio Optimization
There are several different methods to treat uncertainty in literacy. First, sensitivity analysis which is a post-optimization method analyzing stability of generated solutions. Second, stochastic programming is a modeling approach, and this method is limited to that the uncertainty is stochastic in nature. Third, “Robust Mathematical Programming” is that a candidate solutions allowing to viola...
متن کاملSemidefinite and Second Order Cone Programming Seminar Fall 2012 Lecture 10 Instructor : Farid Alizadeh Scribe
1 Overview In this lecture, we show that a number of sets and functions related to the notion of sum-of-squares (SOS) are SD-representable. We will start with positive polynomials. Then, we introduce a general algebraic framework in which the notion of sum-of-squares can be formulated in very general setting. Recall the cone of nonnegative univariate polynomials: P 2d [t] = p(t) = p 0 + p 1 t +...
متن کاملSemidefinite and Second Order Cone Programming Seminar
Image is represented by an undirected weighted graph G = (V, E) where vertices i ∈ V = {1, . . . , n} correspond to image features, and edges (i, j) ∈ E have weights w(i, j) : V × V 7→ R that reflect pairwise similarity between features. To segment an image, we wish to partition nodes V into two disjoint coherent sets S and S̄ = V \ S. This means that edges within the same set should have high w...
متن کامل