A standard quadratic optimization problem (StQP) consists in minimizing a quadratic form over a simplex. A number of problems can be transformed into a StQP, including the general quadratic problem over a polytope and the maximum clique problem in a graph. In this paper we present several polynomial-time bounds for StQP ranging from very simple and cheap ones to more complex and tight construct...

A multitask learning framework is developed for discriminative classification and regression where multiple large-margin linear classifiers are estimated for different prediction problems. These classifiers operate in a common input space but are coupled as they recover an unknown shared representation. A maximum entropy discrimination (MED) framework is used to derive the multitask algorithm w...

The roof dual bound for quadratic unconstrained binary optimization is the basis for several methods for efficiently computing the solution to many hard combinatorial problems. It works by constructing the tightest possible lower-bounding submodular function, and instead of minimizing the original objective function, the relaxation is minimized. However, for higher-order problems the technique ...

In this paper, we aim at minimizing the actuator torques of robots working on production lines by adding to the mechanism dynamic equilibrators based on nonlinear springs, that work in parallel with the joints. We propose a method to simultaneously optimize the trajectory of the robot and the force profiles of the nonlinear springs to minimize the actuator torques. First, we express the traject...

the problem of discrimination between two stationary ar(p) plus noise processes is consideredwhen the noise process are different in two models. the discrimination rule leads to a quadratic form withcumbersome matrices. an approximate and analytic form is given to distribution of the discriminant. thesimulation study has been used to show the performance of discrimination rule. the cumulants of...

We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers–Ulam–Rassias stability of the quadratic functional equation f(x + y) + f(x − y) = 2f(x) + 2f(y). Our result can be regarded as a generalization of the stability phenomenon in the framework of normed spaces. We also prove a generalized version of fuzzy stability o...

A, B, C = state-space matrices a = acceleration due to linear-quadratic-regulatorand artificial-potential-field-determined control effort aAPF = acceleration due to artificial-potential-fielddetermined control effort aLQR = acceleration due to linear-quadratic-regulatordetermined control effort am = maximum acceleration aobs = acceleration of chaser spacecraft toward an obstacle ax;y;z = accele...

Three approaches are currently used for devising identity-based encryption schemes. They build on pairings, quadratic residues (QR), and lattices, respectively. Among them, the QR-based scheme proposed by Cocks in 2001 is notable in that it works in standard RSA groups: its security relies on the standard quadratic residuosity assumption. But is has also a number of deficiencies, some of them h...

In this paper we propose a smoothing Newton-type algorithm for the problem of minimizing a convex quadratic function subject to finitely many convex quadratic inequality constraints. The algorithm is shown to converge globally and possess stronger local superlinear convergence. Preliminary numerical results are also reported.

It is shown that an even partition A∪B of the set R = {1, 2, . . . , p− 1} of positive residues modulo an odd prime p is the partition into quadratic residues and quadratic non-residues if and only if the elements of A and B satisfy certain additive properties, thus providing a purely additive characterization of the set of quadratic residues. 1 Additive properties of quadratic residues An inte...