In order to verify semialgebraic programs, we automatize the Floyd/Naur/Hoare proof method. The main task is to automatically infer valid invariants and rank functions. First we express the program semantics in polynomial form. Then the unknown rank function and invariants are abstracted in parametric form. The implication in the Floyd/Naur/Hoare verification conditions is handled by abstractio...

There are variety of methods to solve the localization problem and among them semi-definite programming based methods have shown great performance in both complexity and accuracy aspects. In this paper, we introduce a class of less noise-sensitive relaxation to reduce the complexity of the SDP-based methods. We apply our relaxation to Edge-based Semidefinite Programming method (ESDP) and the re...

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton d...

In non-cooperative scenarios, the estimation of direct sequence spread spectrum (DS-SS) signals has to be done in a blind manner. In this letter, we consider the spreading sequence estimation problem for DS-SS signals. First, the maximum likelihood estimate (MLE) of spreading sequence is derived, then a semidefinite relaxation (SDR) approach is proposed to cope with the exponential complexity o...

In this paper, we propose a coordinate descent approach to low-rank structured semidefinite programming. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and typically attains an order of magnitude or better improvement in optimization performance over the current state of the art. We show that for certain problems, the method is strictly ...

We propose a new relaxation scheme for the MAX-CUT problem using second-order cone programming. We construct relaxation problems to reflect the structure of the original graph. Numerical experiments show that our relaxation gives better bounds than those based on the spectral decomposition proposed by Kim and Kojima [16], and that the efficiency of the branch-and-bound method using our relaxati...

Today we consider a semidefinite programming relaxation algorithm for SBM and derive conditions for exact recovery. The main ingredient for the proof will be duality theory.

A robust truss optimization scheme, as well as an optimization algorithm, is presented based on the robustness function. Under the uncertainties of external forces based on the info-gap model, the maximization problem of robustness function is formulated as the optimization problem with infinitely many constraint conditions. By using a semidefinite relaxation technique, we reformulate the prese...

Semidefinite relaxations are a powerful tool for approximately solving combinatorial optimization problems such as MAX-CUT and the Grothendieck problem. By exploiting a bounded rank property of extreme points in the semidefinite cone, we make a sub-constant improvement in the approximation ratio of one such problem. Precisely, we describe a polynomial-time algorithm for the positive semidefinit...

While semidefinite relaxations are known to deliver good approximations for combinatorial optimization problems like graph bisection, their practical scope is mostly associated with small dense instances. For large sparse instances, cutting plane techniques are considered the method of choice. These are also applicable for semidefinite relaxations via the spectral bundle method, which allows to...