Zoutendijk Method Of Feasible Directions Research Articles

Resource-saving scheduling scheme for centralized target tracking in multiple radar system under automatic blanket jamming

This paper investigates the problem of Joint Radar Node Selection and Power Allocation (JRNSPA) in the Multiple Radar System (MRS) in the blanket jamming environment. Each radar node independently tracks moving target and subsequently transmits the raw observation data to the fusion center, which formulates a centralized tracking network structure. In order to establish a practical blanket jamming environment, we suppose that each target carries the self-defense jammer which automatically implements blanket jamming to the radar nodes that exceed the preset interception probability. Subsequently, the Predicted Conditional Cramer-Rao Lower Bound (PC-CRLB) is derived and utilized as the tracking accuracy criterion. Aimed at ensuring both the tracking performance and the Low Probability of Intercept (LPI) performance, the resource-saving scheduling model is formulated to minimize the transmit power consumption while meeting the requirements of tracking accuracy. Finally, the Modified Zoutendijk Method Of Feasible Directions (MZMFD)-based two-stage solution technique is adopted to solve the formulated non-convex optimization model. Simulation results show the effectiveness of the proposed JRNSPA scheme.

Energy Efficient Resource Allocation for MSCA Enabled CoMP in HetNets

A novel multi-stream carrier aggregation (MSCA) enabled coordinated multi-point (CoMP) framework in heterogeneous cellular networks (HetNets) is proposed. Our objective is to maximize the energy efficiency (EE) of the proposed framework by jointly optimizing base station (BS) clustering, user association, sub-carrier assignment and power allocation. The formulated problem is proved to be NP-hard. By analyzing the structure of the original problem, we decouple it into power allocation sub-problem and sub-carrier assignment sub-problem. For the power allocation sub-problem, we propose sequential minimization technique and Zoutendijk feasible direction method to find the optimal power allocation with fixed sub-carrier assignment. For the sub-carrier assignment sub-problem, we propose genetic algorithm (GA) to represent the BS clustering and sub-carrier assignment, and design two GA based joint optimization frameworks. One is using the power allocation algorithm for fitness evaluation and guiding the evolution of GA. Another is optimizing these two sub-problems in an iterative manner, whereas the optimal sub-carrier assignment is updated timely as any change of the power allocation. Numerical results validate the feasibility, fast convergence, and flexibility of the proposed algorithm, and is superior to conventional MSCA or CoMP enabled HetNets.

Scaled accuracy based power allocation for multi-target tracking with colocated MIMO radars

A colocated MIMO radar system can offer enhanced multi-target tracking (MTT) performance due to its agile multibeam working mode, in which multiple transmit beams are synthesized simultaneously using probing signals from individual colocated transmitters. To ensure that the limited transmitting power resource of a colocated MIMO radar is exploited effectively, in this paper, a scaled accuracy based power allocation framework (SA-PAF) is proposed for MTT. For a given total power budget, an overall MTT performance objective is optimized by adjusting the transmit power of each beam based on the feedback information in the tracking recursion cycle. An overall cost function (OCF), which is a combination of individual target cost functions (ITCF), is designed as the overall performance objective of the optimization problem. The necessity of ITCF is due to the fact that the impact of the state estimation error on the objective function should be different for each target due to its unique importance (or threat level) and the corresponding tracking accuracy requirement among multiple targets. The proposed OCF can quantify the global MTT performance while properly taking into account different target priorities through ITCFs. To formulate the OCF based framework as an optimization problem, we use the exponential function that employs the posterior Cramér–Rao lower bound (PCRLB) as the tracking performance measure as the instantiation of ITCF. It is shown that the proposed scheme is non-convex in the presence of a clutter. Then, the Zoutendijk method of feasible directions (ZMFD) is used to find the suboptimal power allocation solutions. Simulation results verify the superiority of the proposed power allocation algorithm in terms of achieving the effective overall performance of MTT while taking into account the differences targets priorities.

Hybrid Biogeography-based Optimization Algorithm for Solving Nonlinear Bilevel Programming

The article deals with a class of nonlinear bilevel programming problems in which the follower’s objective is a quasi-concave function, and a new hybrid biogeography-based optimization algorithm is proposed to search for the value of the leader’s variables. First, an extreme point searching approach is constructed to obtain the optimal solution of the follower’s programming. An efficient mutation operator is then designed by using Zoutendijk feasible direction method so that it can generate high quality potential offspring. Furthermore, a new fitness function is established that can be easily used to force the individuals moving toward the feasible region and improve the feasible solutions gradually. Under some assumptions, theoretical analysis of the algorithm has been presented. Finally, to verify the effectiveness of the algorithm, numerical experiments on 8 test problems are made and performance analysis verify the proposed algorithm can converge to the global optimal solution of bilevel programming problems.

A Conjugate Gradient Type Method for the Nonnegative Constraints Optimization Problems

We are concerned with the nonnegative constraints optimization problems. It is well known that the conjugate gradient methods are efficient methods for solving large-scale unconstrained optimization problems due to their simplicity and low storage. Combining the modified Polak-Ribière-Polyak method proposed by Zhang, Zhou, and Li with the Zoutendijk feasible direction method, we proposed a conjugate gradient type method for solving the nonnegative constraints optimization problems. If the current iteration is a feasible point, the direction generated by the proposed method is always a feasible descent direction at the current iteration. Under appropriate conditions, we show that the proposed method is globally convergent. We also present some numerical results to show the efficiency of the proposed method.

Packing equal circles into a circle with circular prohibited areas

The paper considers the problem of packing a maximal number of identical circles of a given radius into a multiconnected domain. The domain is a circle with prohibited areas to be finite unions of circles of given radii. We construct a mathematical model of the problem and investigate its characteristics. The starting points are constructed in a random way or on the ground of the hexagonal lattice. To find the local maxima, a modification of the Zoutendijk method of feasible directions and a strategy of active inequalities are applied. We compare our results with the benchmark instances of packing circles into circular and annular containers. A number of numerical examples are given.

Packing congruent spheres into a multi‐connected polyhedral domain

AbstractIn this paper, we have considered a problem of packing the maximal number of congruent spheres into a multi‐connected polyhedral domain. A mathematical model of the problem has been formulated on the basis of Φ functions. This paper proposes a special way of constructing starting points. To find local maxima, a modification of the Zoutendijk method of feasible directions and a strategy of active inequalities are used. We developed a special approach to search for an approximation to a global maximum. A number of numerical examples are also provided.

Solving an optimization packing problem of circles and non-convex polygons with rotations into a multiply connected region

This paper deals with the packing problem of circles and non-convex polygons, which can be both translated and rotated into a strip with prohibited regions. Using the Φ-function technique, a mathematical model of the problem is constructed and its characteristics are investigated. Based on the characteristics, a solution approach to the problem is offered. The approach includes the following methods: an optimization method by groups of variables to construct starting points, a modification of the Zoutendijk feasible direction method to search for local minima and a special non-exhaustive search of local minima to find an approximation to a global minimum. A number of numerical results are given. The numerical results are compared with the best known ones.

Packing congruent hyperspheres into a hypersphere

The paper considers a problem of packing the maximal number of congruent nD hyperspheres of given radius into a larger nD hypersphere of given radius where n = 2, 3, . . . , 24. Solving the problem is reduced to solving a sequence of packing subproblems provided that radii of hyperspheres are variable. Mathematical models of the subproblems are constructed. Characteristics of the mathematical models are investigated. On the ground of the characteristics we offer a solution approach. For n ? 3 starting points are generated either in accordance with the lattice packing of circles and spheres or in a random way. For n > 3 starting points are generated in a random way. A procedure of perturbation of lattice packings is applied to improve convergence. We use the Zoutendijk feasible direction method to search for local maxima of the subproblems. To compute an approximation to a global maximum of the problem we realize a non-exhaustive search of local maxima. Our results are compared with the benchmark results for n = 2. A number of numerical results for 2 ? n ? 24 are given.

Packing identical spheres into a cylinder

AbstractThe paper deals with the optimization problem of packing identical spheres into a cylinder of minimal height. A mathematical model of the problem is constructed and its characteristics are considered. On the ground of characteristics, a strategy of searching for an approximation to a global minimum is offered. The strategy includes a special search tree construction, a modification of the Zoutendijk method of feasible directions to calculate local minima, and a modification of the decremental neighborhood method to search for an approximation to a global minimum. Numerical examples and performance analysis of solutions are given. On the basis of the mathematical model and numerical experiment, a number of conclusions are drawn.

Design of time-limited pulses

An approach for designing time-limited transmit pulses is proposed. In the approach, a time-limited pulse is represented by a weighted sum of cosine functions whose frequencies are integer multiples of one over the time duration of the transmit pulse. The weighting coefficients are derived to minimize the mean square error of received symbols for a given symbol timing offset, while restricting the out-of-band energy to a predefined level. The minimization is numerically performed by using the Zoutendijk's feasible direction method. Performance comparison results are presented showing that the pulses derived by this approach not only have smaller mean square errors, but also smaller symbol error probabilities for BPSK signaling compared to the time-truncated versions of conventional square-root Nyquist pulses.

Exergoeconomic optimisation of a Kalina cycle for power generation

It is shown that the use of an ammonia-water Kalina absorption power cycle as a bottoming cycle for a cogeneration plant may result in an economic advantage. This cycle was optimised using as a goal function the exergoeconomic unitary cost of the electricity produced by both the cogeneration plant and the absorption cycle. The Zoutendijk method of feasible directions was used for this optimisation. The results obtained show that the generated net power increases in 3.26% and the unitary cost of electricity diminishes in 3.14%.

A superlinearly convergent method of feasible directions

Method of feasible directions (MFD) is one of the most important methods for solving engineering optimization problems. There exist two types of MFD: one has at most a linear convergence rate and the other has a superlinear convergence rate. The former type includes Zoutendijk's MFD, Topkis–Veinott's MFD, Pironneau–Polak's MFD, Cawood–Kostreva's Norm-Relaxed MFD, and a modified MFD. The latter includes Panier–Tits' FSQP approaches. However, the price of the superlinearly convergent MFD for achieving superlinearity is rather high computational cost per single iteration. This paper presents an algorithm based on the modified MFD. The theoretical analysis shows that this algorithm is locally superlinearly convergent. This algorithm has attained the same convergence rate as FSQP while it only needs to solve two subproblems instead of three subproblems in FSQP. Hence, this algorithm should be computationally more efficient than FSQP.

Algorithmic modeling of TES processes

TES (transform-expand-sample) is a versatile class of stationary stochastic processes which can model arbitrary marginals, a wide variety of autocorrelation functions, and a broad range of sample path behaviors. TES parameters are of two kinds: the first kind is used for the exact fitting of the empirical distribution (histogram), while the second kind is used for approximating the empirical autocorrelation function. Parameters of the first kind are easy to determine algorithmically, but those of the second kind require a hard heuristic search on a large parametric function space. This paper describes an algorithmic procedure which can replace the heuristic search, thereby largely automating TES modeling. The algorithm is cast in nonlinear programming setting with the objective of minimizing a weighted sum of squared differences between the empirical autocorrelations and their candidate TES model counterparts. It combines a brute-forte search with steepest-descent nonlinear programming using Zoutendijk's feasible direction method. Finally, we illustrate the efficacy of our approach via three examples: two from the domain of VBR (variable bit rate) compressed video and one representing results from a laser intensity experiment. >