A nonmonotone trust-region method of conic model for unconstrained optimization

AbstractIn this paper, we present a nonmonotone trust-region method of conic model for unconstrained optimization. The new method combines a new trust-region subproblem of conic model proposed in [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231] with a nonmonotone technique for solving unconstrained optimization. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the method of [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231]

Constrained Phase Noise Estimation in OFDM Using Scattered Pilots Without Decision Feedback

In this paper, we consider an OFDM radio link corrupted by oscillator phase noise in the receiver, namely the problem of estimating and compensating for the impairment. To lessen the computational burden and delay incurred onto the receiver, we estimate phase noise using only scattered pilot subcarriers, i.e., no tentative symbol decisions are used in obtaining and improving the phase noise estimate. In particular, the phase noise estimation problem is posed as an unconstrained optimization problem whose minimizer suffers from the so-called amplitude and phase estimation error. These errors arise due to receiver noise, estimation from limited scattered pilot subcarriers and estimation using a dimensionality reduction model. It is empirically shown that, at high signal-to-noise-ratios, the phase estimation error is small. To reduce the amplitude estimation error, we restrict the minimizer to be drawn from the so-called phase noise geometry set when minimizing the cost function. The resulting optimization problem is a non-convex program. However, using the S-procedure for quadratic equalities, we show that the optimal solution can be obtained by solving the convex dual problem. We also consider a less complex heuristic scheme that achieves the same objective of restricting the minimizer to the phase noise geometry set. Through simulations, we demonstrate improved coded bit-error-rate and phase noise estimation error performance when enforcing the phase noise geometry. For example, at high signal-to-noise-ratios, the probability density function of the phase noise estimation error exhibits thinner tails which results in lower bit-error-rate

Projection methods in conic optimization

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear conic optimization, and applications in polynomial optimization. This is a presentation of the material of several recent research articles; we aim here at clarifying the ideas, presenting them in a general framework, and pointing out important techniques

Capabilities and applications of the Program to Optimize Simulated Trajectories (POST). Program summary document

The capabilities and applications of the three-degree-of-freedom (3DOF) version and the six-degree-of-freedom (6DOF) version of the Program to Optimize Simulated Trajectories (POST) are summarized. The document supplements the detailed program manuals by providing additional information that motivates and clarifies basic capabilities, input procedures, applications and computer requirements of these programs. The information will enable prospective users to evaluate the programs, and to determine if they are applicable to their problems. Enough information is given to enable managerial personnel to evaluate the capabilities of the programs and describes the POST structure, formulation, input and output procedures, sample cases, and computer requirements. The report also provides answers to basic questions concerning planet and vehicle modeling, simulation accuracy, optimization capabilities, and general input rules. Several sample cases are presented