We present a row-by-row (RBR) method for solving semidefinite programming (SDP) problem based on solving a sequence of problems obtained by restricting the n-dimensional positive semidefinite constraint on the matrix X. By fixing any (n − 1)-dimensional principal submatrix of X and using its (generalized) Schur complement, the positive semidefinite constraint is reduced to a simple second-order...

We present Spatiotemporal Derivative Pattern (SDP), a descriptor for dynamic textures. Using local continuous circular and spiral neighborhoods within video segments, SDP encodes the derivatives of the directional spatiotemporal patterns into a binary code. The main strength of SDP is that it uses fewer frames per segment to extract more distinctive features for efficient representation and acc...

One of the fundamental clustering problems is to assign n points into k clusters based on the minimal sum-of-squares(MSSC), which is known to be NP-hard. In this paper, by using matrix arguments, we first model MSSC as a so-called 0-1 semidefinite programming (SDP). The classical K-means algorithm can be interpreted as a special heuristics for the underlying 0-1 SDP. Moreover, the 0-1 SDP model...

We introduce a new relaxation framework for nonconvex quadratically constrained quadratic programs (QCQPs). In contrast to existing relaxations based on semidefinite programming (SDP), our relaxations incorporate features of both SDP and second order cone programming (SOCP) and, as a result, solve more quickly than SDP. A downside is that the calculated bounds are weaker than those gotten by SD...

While invoicing currency has been extensively studied in open-economy macroeconomics, Dotsey and Duarte (2011) suggest that the currency denomination of exports does not matter because standard invoicing currency regimes such as producer currency pricing (PCP) and local currency pricing (LCP) generate similar aggregate responses. However, this paper demonstrates the importance of invoicing curr...

The single-row facility layout problem (SRFLP) is concerned with finding the optimal linear placement of n departments with different lengths in a straight line. It is typically achieved by minimizing the cost associated with the interactions between the departments. The semidefinite programming (SDP) relaxation model that incorporates cutting planes proposed recently by Anjos, Kennings, and Va...

A polynomial optimization problem (POP) consists of minimizing a multivariate real polynomial on a semi-algebraic set K described by polynomial inequalities and equations. In its full generality it is a non-convex, multi-extremal, difficult global optimization problem. More than an decade ago, J. B. Lasserre proposed to solve POPs by a hierarchy of convex semidefinite programming (SDP) relaxati...

In this paper, we introduce a transformation that converts a class of linear and nonlinear semidefinite programming (SDP) problems into nonlinear optimization problems over “orthants” of the form <++ × <N , where n is the size of the matrices involved in the problem and N is a nonnegative integer dependent upon the specific problem. For example, in the case of the SDP relaxation of a MAXCUT pro...