Invited Session Thu.3.H 2036

Thursday, 15:15 - 16:45 h, Room: H 2036

Cluster 4: Conic programming [...]

Conic optimization and signal processing applications


Chair: Anthony Man-Cho So



Thursday, 15:15 - 15:40 h, Room: H 2036, Talk 1

Senshan Ji
Approximating a KKT point of Schatten p-quasi-norm minimization in polynomial time, with applications to sensor network localization

Coauthor: Anthony Man-Cho So


In this talk, we consider the Schatten p-quasi norm minimization problem, which has previously found applications in compressed sensing and
matrix completion. We propose a potential reduction algorithm to approximate a KKT point of the Schatten p-quasi norm minimization problem. We show that our algorithm is a fully polynomial-time approximation scheme, taking no more than O(n⁄pεlog1⁄ε) iterations to reach an ε-KKT point or global minimizer. We then apply the algorithm to the sensor network localization problem. Our numerical results show that in many cases, the proposed algorithm can achieve better results than the standard semidefinite relaxation of the problem.



Thursday, 15:45 - 16:10 h, Room: H 2036, Talk 2

Wing-Kin Ma
Semidefinite relaxation in wireless communications: Forefront developments, advances and challenges


Semidefinite relaxation (SDR) is well-known to be an efficient high-performance technique for approximating a host of hard, nonconvex optimization problems. And one of its most recognized applications is probably MAXCUT. In fact, SDR has also made its way to signal processing and wireless communications, and the impact is tremendous - today we see not only numerous applications, but also new fundamental concepts and theory driven by the applications themselves. This talk will focus on transmit beamforming, now a key topic in communications. I will provide an overview on its scope, which is quite broad (classical multiuser downlinks, unicasting and multicasting, multicell coordinated multiuser downlinks, cognitive radio, physical layer security, relaying, … ). I will then describe some latest advances that link up fundamentally meaningful optimization studies, like chance-constrained optimization, and rank-two SDR. This will be followed by an open discussion on some mysteries and challenges, noticed by researchers in simulations. For example, why does SDR give us a rank-one solution for some hard problems that involve semi-infinite quadratic constraints, seemingly all the time?



Thursday, 16:15 - 16:40 h, Room: H 2036, Talk 3

Yang Yang
Multi-portfolio optimization: A variational inequality approach

Coauthors: Daniel Palomar, Francisco Rubio, Gesualdo Scutari


In this paper, we study the multi-portfolio optimization problem with square-root market impact model
using a game-theoretic approach. Contrary to the linear market impact model, available tools such as potential
game theory are not applicable for the square-root model. We approach this problem using Variational
Inequality, and give a comprehensive and rigorous analysis on the properties of the Nash Equilibrium such
as existence and uniqueness, and devise efficient algorithms with satisfactory convergence property. A
more general game problem where all accounts are subject to global constraints is also studied under the
framework of Variational Inequality.


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