Nonmonotone Stabilization Research Articles

Is the relationship between bank stability, competition, and intervention quality nonlinear? Evidence from North African countries

AbstractThis paper highlights the existence of a nonlinear relationship between bank stability and competition and analyzes the role that government intervention plays in shaping this relationship. We used a sample of 45 banks in North African countries over the period 2005–2019. We applied a semiparametric approach based on penalized spline estimation. The results unveil the specific shape of the competition–stability relationship at different levels of competition; banks reconsider their risk‐taking behavior at each level of competition. This nonmonotonic stability at different levels of competition is attributed to the quality of intervention, which is found to be an important determinant in shaping this relationship. Thus, we explain the dispersion of risk levels among North African banks in part by the quality of regulation in each country and conclude by recommending the strengthening of regulation, supervision and the macro‐prudential framework.

Unravelling the polyethylenimine mediated non-monotonic stability behaviour of silica colloids: the role of competing electrostatic and entropic interactions.

Polymer-mediated interactions play an important role in the stability of colloids and are therefore paramount for both fundamental as well as scientific interests. The stability of colloids in the presence of neutral polymers depends on several parameters such as the adsorbing/non-adsorbing nature, molecular weight, concentration and temperature, and such systems are well studied. However, the stability behaviour of charged colloids in the presence of charged polyelectrolyte involves complex interaction mechanisms and hence needs attention. The present work reports the study of the stability behaviour of negatively charged silica colloids in the presence of cationic polyethylenimine (PEI) polyelectrolyte using small-angle neutron and X-ray scattering. The intriguing non-monotonic stability behaviour of silica colloids is observed with varying concentrations of PEI. In the low and intermediate PEI concentration regimes, electrosorption of PEI on the silica colloids causes partial screening of charges, leading to aggregation of colloids. The DLVO interaction potential at low and intermediate concentrations of PEI exhibit a reduced repulsion barrier which is responsible for aggregation. In the high concentration regime, the entropic interaction between the free PEI molecules and PEI decorated silica colloids leads to depletion re-stabilization. The combination of DLVO potential and adsorbed PEI mediated enhanced depletion repulsion in the presence of free PEI gives rise to an increased repulsion barrier responsible for the re-stabilization at high PEI concentrations.

Novel Non-monotonic Lyapunov-Krasovskii Based Stability Analysis and Stabilization of Discrete State-delay System

This paper proposes a novel less-conservative non-monotonic Lyapunov-Krasovskii stability approach for stability analysis of discrete time-delay systems. In this method, monotonically decreasing requirements of the Lyapunov-Krasovskii method are replaced with non-monotonic ones. The Lyapunov-Krasovskii functional is allowed to increase in some steps, but the overall trend should be decreasing. The model of practical systems used for stability analysis usually contain uncertainty. Therefore, firstly a non-monotonic stability condition is derived for certain discrete time-delay systems, then robust non-monotonic stability conditions are proposed for uncertain systems. Finally, a novel stabilization algorithm is derived based on the introduced non-monotonic stability condition. The Lyapunov-Krasovskii functional and the controller are obtained by solving a set of linear matrix inequalities (LMI) or iterative LMI based nonlinear minimization. The proposed theorems are first evaluated by some numerical examples, and then by simulation and implementation on the pH neutralizing process plant.

Optimal fuzzy controller based on non-monotonic Lyapunov function with a case study on laboratory helicopter

ABSTRACTThis paper presents a new approach to design an observer-based optimal fuzzy state feedback controller for discrete-time Takagi–Sugeno fuzzy systems via LQR based on the non-monotonic Lyapunov function. Non-monotonic Lyapunov stability theorem proposed less conservative conditions rather than common quadratic method. To compare with optimal fuzzy feedback controller design based on common quadratic Lyapunov function, this paper proceeds reformulation of the observer-based optimal fuzzy state feedback controller based on common quadratic Lyapunov function. Also in both methodologies, the dependence of optimisation problem on initial conditions is omitted. As a practical case study, the controllers are implemented on a laboratory twin-rotor helicopter to compare the controllers' performance.

Stability of a Switched Mode Power Amplifier Interface for Power Hardware-in-the-Loop

Power hardware-in-the-loop (PHIL) is an attractive, real-time system testing and validation technique. Virtual models can be replaced with physical equipment to emulate system integration testing, and perform model validation without the cost and risk of a full scale power system. Power amplifiers are the principal components that facilitate the power interface between the physical and the virtual systems. This necessary interfacing introduces dynamics that do not exist in the real system and is the source of stability and accuracy issues affecting PHIL applications. This paper presents a stability analysis of a practical PHIL system based on the ideal transformer model interface algorithm that utilizes a voltage source converter for power amplification. A systematic approach to evaluate the expected stability characteristics of PHIL experiments is developed. The analysis in this paper shows that in a practical system, the power amplifier's filter, sampling, and measurement filtering are all shown to influence the stability in a counterintuitive way, leading to a nonmonotonic stability characteristic. An experimental PHIL platform based on a real-time digital simulator real-time computer has been used to validate the analysis and confirm the effects of the practical interface. Switching dead-time is also shown to have a significant stabilizing effect.

An active set feasible method for large-scale minimization problems with bound constraints

We are concerned with the solution of the bound constrained minimization problem {minf(x), l?x?u}. For the solution of this problem we propose an active set method that combines ideas from projected and nonmonotone Newton-type methods. It is based on an iteration of the form x k+1=[x k +? k d k ]?, where ? k is the steplength, d k is the search direction and [?]? is the projection operator on the set [l,u]. At each iteration a new formula to estimate the active set is first employed. Then the components $d_{N}^{k}$ of d k corresponding to the free variables are determined by a truncated Newton method, and the components $d_{A}^{k}$ of d k corresponding to the active variables are computed by a Barzilai-Borwein gradient method. The steplength ? k is computed by an adaptation of the nonmonotone stabilization technique proposed in Grippo et al. (Numer. Math. 59:779---805, 1991). The method is a feasible one, since it maintains feasibility of the iterates x k , and is well suited for large-scale problems, since it uses matrix-vector products only in the truncated Newton method for computing $d_{N}^{k}$ . We prove the convergence of the method, with superlinear rate under usual additional assumptions. An extensive numerical experimentation performed on an algorithmic implementation shows that the algorithm compares favorably with other widely used codes for bound constrained problems.

A nonmonotone globalization algorithm with preconditioned gradient path for unconstrained optimization

The aim of this paper is to incorporate the preconditioned gradient path in a nonmonotone stabilization algorithm for unconstrained optimization. The global convergence and locally superlinear convergence are established for this class of algorithms. Finally, we report in details the numerical results which show the effectiveness of the proposed algorithm.

A nonmonotone truncated Newton–Krylov method exploiting negative curvature directions, for large scale unconstrained optimization

We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative curvature direction. A test based on the quadratic model of the objective function is used to select the most promising between the two search directions. Both the latter selection rule and the CG stopping criterion for approximately solving Newton’s equation, strongly rely on conjugacy conditions. An appropriate linesearch technique is adopted for each search direction: a nonmonotone stabilization is used with the approximate Newton step, while an Armijo type linesearch is used for the negative curvature direction. The proposed algorithm is both globally and superlinearly convergent to stationary points satisfying second order necessary conditions. We carry out a significant numerical experience in order to test our proposal.

An Active Set Newton Algorithm for Large-Scale Nonlinear Programs with Box Constraints

A new algorithm for large-scale nonlinear programs with box constraints is introduced. The algorithm is based on an efficient identification technique of the active set at the solution and on a nonmonotone stabilization technique. It possesses global and superlinear convergence properties under standard assumptions. A new technique for generating test problems with known characteristics is also introduced. The implementation of the method is described along with computational results for large-scale problems.

A multiclass network with non-linear, non-convex, non-monotonic stability conditions

We consider a stochastic queueing network with fixed routes and class priorities. The vector of class sizes forms a homogeneous Markov process of countable state space Z_+^6. The network is said “stable” (resp.“unstable”) if this Markov process is ergodic (resp. transient). The parameters are the traffic intensities of the different classes. An unusual condition of stability is obtained thanks to a new argument based on the characterization of the “essential states”. The exact stability conditions are then detected thanks to an associated fluid network: we identify a zone of the parameter space in which diverging, fluid paths appear. In order to show that this is a zone of instability (and that the network is stable outside this zone), we resort to the criteria of ergodicity and transience proved by Malyshev and Menshikov for reflected random walks in Z_+^N (Malyshev and Menshikov, 1981). Their approach allows us to neglect some “pathological” fluid paths that perturb the dynamics of the fluid model. The stability conditions thus determined have especially unusual characteristics: they have a quadratic part, the stability domain is not convex, and increasing all the service rates may provoke instability (Theorem 1.1 and section 7).

Nonmonotone curvilinear line search methods for unconstrained optimization

We present a new algorithmic framework for solving unconstrained minimization problems that incorporates a curvilinear linesearch. The search direction used in our framework is a combination of an approximate Newton direction and a direction of negative curvature. Global convergence to a stationary point where the Hessian matrix is positive semidefinite is exhibited for this class of algorithms by means of a nonmonotone stabilization strategy. An implementation using the Bunch-Parlett decomposition is shown to outperform several other techniques on a large class of test problems.

A class of nonmonotone stabilization trust region methods

A class of trust region methods in unconstrained optimization is presented, by adopting a nonmonotone stabilization strategy. Under some regularity conditions, the convergence properties of these methods are discussed. Extensive numerical results which are reported show that these methods are very efficient.

Nonmonotone stabilization methods for nonlinear equations

We are concerned with defining new globalization criteria for solution methods of nonlinear equations. The current criteria used in these methods require a sufficient decrease of a particular merit function at each iteration of the algorithm. As was observed in the field of smooth unconstrained optimization, this descent requirement can considerably slow the rate of convergence of the sequence of points produced and, in some cases, can heavily deteriorate the performance of algorithms. The aim of this paper is to show that the global convergence of most methods proposed in the literature for solving systems of nonlinear equations can be obtained using less restrictive criteria that do not enforce a monotonic decrease of the chosen merit function. In particular, we show that a general stabilization scheme, recently proposed for the unconstrained minimization of continuously differentiable functions, can be extended to methods for the solution of nonlinear (nonsmooth) equations. This scheme includes different kinds of relaxation of the descent requirement and opens up the possibility of describing new classes of algorithms where the old monotone linesearch techniques are replace with more flexible nonmonotone stabilization procedures. As in the case of smooth unconstrained optimization, this should be the basis for defining more efficient algorithms with very good practical rates of convergence.

A class of nonmonotone stabilization methods in unconstrained optimization

This paper deals with the solution of smooth unconstrained minimization problems by Newton-type methods whose global convergence is enforced by means of a nonmonotone stabilization strategy. In particular, a stabilization scheme is analyzed, which includes different kinds of relaxation of the descent requirements. An extensive numerical experimentation is reported.

A quasi-discrete Newton algorithm with a nonmonotone stabilization technique

In this paper, we define an unconstrained optimization algorithm employing only first-order derivatives, in which a nonmonotone stabilization technique is used in conjunction with a quasidiscrete Newton method for the computation of the search direction. Global and superlinear convergence is proved, and numerical results are reported.