Analytic Solution for Hypersonic Flow Past a Slender Elliptic Cone Using Second-Order Perturbation Approximations

Hypersonic flow past slender bodies in dispersive hydrodynamics

The problem of two-dimensional steady hypersonic flow past a slender body is formulated for dispersive media. It is shown that for the hypersonic flow, the original 2+ 0 boundary-value problem is asymptotically equivalent to the 1+ 1 piston problem for the fully nonlinear flow in the same physical system, which allows one to take advantage of the analytic methods developed for one-dimensional s...

Second Order Cone Programming Formulations for Handling Data with Perturbation

Ordinal regression problem and general multi-class classification problem are important and on-going research subject in machine learning. Support vector ordinal regression machine (SVORM) is an effective method for ordinal regression problem and has been used to deal with general multi-class classification problem. Up to now it is always assumed implicitly that the training data are known exac...

Waveform Design using Second Order Cone Programming in Radar Systems

Transmit waveform design is one of the most important problems in active sensing and communication systems. This problem, due to the complexity and non-convexity, has been always the main topic of many papers for the decades. However, still an optimal solution which guarantees a global minimum for this multi-variable optimization problem is not found. In this paper, we propose an attracting met...

On Polyhedral Approximations of the Second-Order Cone

We demonstrate that a conic quadratic problem min x { ex ∣Ax ≥ b, ‖A`x− b`‖2 ≤ c` x− d`, ` = 1, ...,m } , ‖y‖2 = √ yT y, (CQP) is “polynomially reducible” to Linear Programming. We demonstrate this by constructing, for every ∈ (0, 12 ], an LP program (explicitly given in terms of and the data of (CQP)) min x,u { ex ∣P ( x u ) + p ≥ 0 } (LP) with the following properties: (i) the number dim x+ d...

Mortar Finite Volume Element Approximations of Second Order Elliptic Problems

Perturbation analysis of second-order cone programming problems

We discuss first and second order optimality conditions for nonlinear second-order cone programming problems, and their relation with semidefinite programming problems. For doing this we extend in an abstract setting the notion of optimal partition. Then we state a characterization of strong regularity in terms of second order optimality conditions.