Recursive Optimization Research Articles

Recursive utility optimization with concave coefficients

This paper concerns the recursive utility maximization problem. We assume that the coefficients of the wealth equation and the recursive utility are concave. Then some interesting and important cases with nonlinear and nonsmooth coefficients satisfy our assumption. After given an equivalent backward formulation of our problem, we employ the Fenchel-Legendre transform and derive the corresponding variational formulation. By the convex duality method, the primal sup-inf problem is translated to a dual minimization problem and the saddle point of our problem is derived. Finally, we obtain the optimal terminal wealth. To illustrate our results, three cases for investors with ambiguity aversion are explicitly worked out under some special assumptions.

The Dual Approach to Recursive Optimization: Theory and Examples

We develop a recursive dual method for solving dynamic economic problems. The method uses a Lagrangian to pair a dynamic recursive economic problem with a dual problem. We show that such dual problems can be recursively decomposed with costates (i.e., Lagrange multipliers on laws of motion) functioning as state variables. In dynamic contracting and policy settings, the method often replaces an endogenous state space of forward†looking utilities with an exogenously given state space of costates. We provide a principle of optimality for dual problems and give conditions under which the dual Bellman operator is a contraction with the optimal dual value function its unique fixed point. We relate economic problems to their duals, address computational issues, and give examples.

Planning, Evaluation and Optimization of Product Design and Manufacturing Technology Chains for New Product and Production Technologies on the Example of Additive Manufacturing

New emerging technologies challenge companies to adapt their product design and production processes constantly. This paper presents an approach that enables companies to manage new technologies by optimizing interdependent product design parameters and manufacturing technology chains. A product is modularized and modelled via parameter sets. Manufacturing technologies are described in a similar model. Possible manufacturing technologies for this product are identified and combined to technology chains. Based on a multi-criteria evaluation, critical product and manufacturing technology parameters are identified and the impact of adapting these parameters is quantified, thus enabling recursive optimization of product and manufacturing technology chain. Thereby, companies can manage new product and manufacturing technologies by assessing their implications and future potential.

ROAC: Recursive optimization of Ant colony assisted perturb and observe for a photo voltaic resonant boost converter

This paper introduces a new Hybrid MPPT algorithm by combining new Ant Colony Optimization (ACO) and Perturb & Observe (P&O) method. The maximum power from a solar panel is extracted from all conditions like solar irradiance variation, temperature variation and partial shading conditions. Ant Colony Optimization (ACO) method tracks maximum power from panel under all variations and Perturb & Observe algorithm used in final stage to achieve faster MPP tracking. This proposed algorithm is implemented both in Simulink and hardware. A 5kWp grid connected solar photovoltaic power plant is designed and implemented for the 15 stage 31 level Cascaded Multilevel Inverter (CMLI) with the Selective harmonic elimination algorithm. From the analysis of results, it is found that the proposed hybrid MPPT provides higher MPP tracking performance in any weather conditions compared with other MPPT algorithms

Optimal Climate Policy for a Pessimistic Social Planner

This paper characterizes the preferences of a pessimistic social planner concerned with the potential costs of extreme, low-probability climate events. This pessimistic attitude is represented by a recursive optimization criterion a la Hansen and Sargent (IEEE Trans Autom Control 40:968–971, 1995) implying that a very sharp and early mitigation effort arises as the optimal climate policy. We find that for sufficiently high levels of risk-aversion an aggressive mitigation policy is chosen even when the discount factor is low. The dynamics of the optimal mitigation policy displays an inverted policy ramp with a sharp and immediate mitigation effort, followed by a gradual reduction until the pollution stock converges towards its long-run equilibrium. We also observe that the initial sharpness of the mitigation effort requires substantial capture and sequestration of carbon from the atmosphere. We extend our analysis showing that when the social planner observes the concentration and emission levels with a time lag, she undertakes a more aggressive policy to reduce the greater degree of uncertainty she faces. Finally, we show under which conditions the optimal mitigation policy dictated by our analysis coincides with that derived using the robustness approach of Hansen and Sargent (Robustness, Princeton University Press, Princeton, 2008).

Parameter identification of a nonlinear model: replicating the motion response of an autonomous underwater vehicle for dynamic environments

This study presents a system identification algorithm to determine the linear and nonlinear parameters of an autonomous underwater vehicle (AUV) motion response prediction mathematical model, utilising the recursive least squares optimisation method. The key objective of the model, which relies solely on propeller thrust, gyro measurements and parameters representing the vehicle hydrodynamic, hydrostatic and mass properties, is to calculate the linear velocities of the AUV in the x, y and z directions. Initially, a baseline mathematical model that represents the dynamics of a Gavia class AUV in a calm water environment was developed. Using a novel technique developed in this study, the parameters within the baseline model were calibrated to provide the motion response in different environmental conditions by conducting a calibration mission in the new environment. The accuracy of the velocity measurements from the calibrated model was substantially greater than those from the baseline model for the tested scenarios with a minimum velocity prediction improvement of 50%. The determined velocities will be used to aid the inertial navigation system (INS) position estimate using a Kalman filter data fusion algorithm when external aiding is unavailable. When an INS is not externally aided or constrained by a mathematical model such as that presented here, the positioning uncertainty can be more than 4% of the distance travelled (assuming a forward speed of 1.6 m s $$^{-1})$$ . The calibrated model is able to compute the position of the AUV within an uncertainty range of around 1.5% of the distance travelled, significantly improving the localisation accuracy.

A Dynamic Event-Triggered Transmission Scheme for Distributed Set-Membership Estimation Over Wireless Sensor Networks.

This paper is concerned with the distributed set-membership estimation for a discrete-time linear time-varying system over a resource-constrained wireless sensor network under the influence of unknown-but-bounded (UBB) process and measurement noise. Sensors collaborate among themselves by exchanging local measurements with only neighboring sensors in their sensing ranges. First, a new dynamic event-triggered transmission scheme (ETS) is developed to schedule the transmission of each sensor's local measurement. In contrast with the majority of existing static ETSs, the newly proposed dynamic ETS can result in larger average interevent times and thus less totally released data packets. Second, a criterion for designing desired event-triggered set-membership estimators is derived such that the system's true state always resides in each sensor's bounding ellipsoidal estimation set regardless of the simultaneous presence of UBB process and measurement noise. Third, a recursive convex optimization algorithm is presented to determine optimal ellipsoids as well as the estimator gain parameters and the event triggering weighting matrix parameter. Furthermore, the proposed dynamic ETS is applied to address the distributed set-membership estimation problem for a discrete-time linear time-varying system with a nonlinearity satisfying a sector constraint. Finally, an illustrative example is given to show the effectiveness and advantage of the developed approach.

Inference of time-delayed gene regulatory networks based on dynamic Bayesian network hybrid learning method.

Gene regulatory networks (GRNs) research reveals complex life phenomena from the perspective of gene interaction, which is an important research field in systems biology. Traditional Bayesian networks have a high computational complexity, and the network structure scoring model has a single feature. Information-based approaches cannot identify the direction of regulation. In order to make up for the shortcomings of the above methods, this paper presents a novel hybrid learning method (DBNCS) based on dynamic Bayesian network (DBN) to construct the multiple time-delayed GRNs for the first time, combining the comprehensive score (CS) with the DBN model. DBNCS algorithm first uses CMI2NI (conditional mutual inclusive information-based network inference) algorithm for network structure profiles learning, namely the construction of search space. Then the redundant regulations are removed by using the recursive optimization algorithm (RO), thereby reduce the false positive rate. Secondly, the network structure profiles are decomposed into a set of cliques without loss, which can significantly reduce the computational complexity. Finally, DBN model is used to identify the direction of gene regulation within the cliques and search for the optimal network structure. The performance of DBNCS algorithm is evaluated by the benchmark GRN datasets from DREAM challenge as well as the SOS DNA repair network in Escherichia coli, and compared with other state-of-the-art methods. The experimental results show the rationality of the algorithm design and the outstanding performance of the GRNs.

Heuristics for Base‐Stock Levels in Multi‐Echelon Distribution Networks

We study inventory optimization for locally controlled, continuous‐review distribution systems with stochastic customer demands. Each node follows a base‐stock policy and a first‐come, first‐served allocation policy. We develop two heuristics, the recursive optimization (RO) heuristic and the decomposition‐aggregation (DA) heuristic, to approximate the optimal base‐stock levels of all the locations in the system. The RO heuristic applies a bottom‐up approach that sequentially solves single‐variable, convex problems for each location. The DA heuristic decomposes the distribution system into multiple serial systems, solves for the base‐stock levels of these systems using the newsvendor heuristic of Shang and Song (2003), and then aggregates the serial systems back into the distribution system using a procedure we call “backorder matching.” A key advantage of the DA heuristic is that it does not require any evaluation of the cost function (a computationally costly operation that requires numerical convolution). We show that, for both RO and DA, changing some of the parameters, such as leadtime, unit backordering cost, and demand rate, of a location has an impact only on its own local base‐stock level and its upstream locations’ local base‐stock levels. An extensive numerical study shows that both heuristics perform well, with the RO heuristic providing more accurate results and the DA heuristic consuming less computation time. We show that both RO and DA are asymptotically optimal along multiple dimensions for two‐echelon distribution systems. Finally, we show that, with minor changes, both RO and DA are applicable to the balanced allocation policy.

Optimization of the GBMV2 implicit solvent force field for accurate simulation of protein conformational equilibria.

Accurate treatment of solvent environment is critical for reliable simulations of protein conformational equilibria. Implicit treatment of solvation, such as using the generalized Born (GB) class of models arguably provides an optimal balance between computational efficiency and physical accuracy. Yet, GB models are frequently plagued by a tendency to generate overly compact structures. The physical origins of this drawback are relatively well understood, and the key to a balanced implicit solvent protein force field is careful optimization of physical parameters to achieve a sufficient level of cancellation of errors. The latter has been hampered by the difficulty of generating converged conformational ensembles of non-trivial model proteins using the popular replica exchange sampling technique. Here, we leverage improved sampling efficiency of a newly developed multi-scale enhanced sampling technique to re-optimize the generalized-Born with molecular volume (GBMV2) implicit solvent model with the CHARMM36 protein force field. Recursive optimization of key GBMV2 parameters (such as input radii) and protein torsion profiles (via the CMAP torsion cross terms) has led to a more balanced GBMV2 protein force field that recapitulates the structures and stabilities of both helical and β-hairpin model peptides. Importantly, this force field appears to be free of the over-compaction bias, and can generate structural ensembles of several intrinsically disordered proteins of various lengths that seem highly consistent with available experimental data. © 2017 Wiley Periodicals, Inc.

Maximum Principle for Markov Regime-Switching Forward–Backward Stochastic Control System with Jumps and Relation to Dynamic Programming

This paper presents a sufficient stochastic maximum principle for a stochastic optimal control problem of Markov regime-switching forward–backward stochastic differential equations with jumps. The relationship between the stochastic maximum principle and the dynamic programming principle in a Markovian case is also established. Finally, applications of the main results to a recursive utility portfolio optimization problem in a financial market are discussed.

Maximum Principle for Forward-Backward Control System Driven by Itô-Lévy Processes under Initial-Terminal Constraints

This paper investigates a stochastic optimal control problem where the control system is driven by Itô-Lévy process. We prove the necessary condition about existence of optimal control for stochastic system by using traditional variational technique under the assumption that control domain is convex. We require that forward-backward stochastic differential equations (FBSDE) be fully coupled, and the control variable is allowed to enter both diffusion and jump coefficient. Moreover, we also require that the initial-terminal state be constrained. Finally, as an application to finance, we show an example of recursive consumption utility optimization problem to illustrate the practicability of our result.

Modeling of battery dynamics and hysteresis for power delivery prediction and SOC estimation

A modeling approach for battery as an Electrical Energy Storage System is proposed in this paper. The model aims to predict non-linear power delivery dynamics, given charge and discharge demand as a controllable input, not only in normal operating range of batteries, but also in extreme cases such as battery over-charging. In order to achieve that, the model is composed of separated voltage and current models. Several non-linear models, including Hammerstein model, non-linear open-circuit voltage characteristics, and Takacs hysteresis model are combined in the voltage and the current model, respectively. The state of charge of the battery can also be estimated in a recursive optimization fashion by the model. The parameterization and estimation methods of the model are described and also demonstrated on experimental data from a lithium iron phosphate (LiFePO4) cell. The experiment validation shows excellent agreement between measured and simulated voltage and current signals provided by the model during both normal operating and over-charging conditions. The contribution of this paper is given by the unique combination of data-based models used to capture linear dynamics, static non-linearity, and non-linear hysteresis effects in a single dynamic voltage/current model to simulate and predict the non-linear dynamic behavior of a battery as an energy storage/delivery system.

Recursive optimization method for monitoring of tension loss in cables of cable-stayed bridges

A simple method is introduced for the detection of damage in the cables of cable-stayed bridges. The approach presented herein utilizes the change in support reactions to localize and quantify the damage in the cables. Determination of support reactions was achieved by detection of the deck element shear forces adjacent to the supports. The analytical approach is formulated as a recursive optimization damage detection technique, in which model updating is employed to account for the changes in the cable stiffness as a result of damage. The efficiency of this approach was evaluated on a reduced-scale cable-stayed bridge in the laboratory. In addition to the laboratory experiments, the proposed approach was also evaluated by simulating damage in an actual cable-stayed bridge through numerical studies. Several different damage scenarios with various levels of damage were considered in the experiments, as well as in the numerical simulations. The results indicate that the proposed method is capable of identifying the location of the damaged cables in the bridge for cases involving up to two damaged cables.

Toward Patients’ Motion Intention Recognition: Dynamics Modeling and Identification of iLeg—An LLRR Under Motion Constraints

In order to implement model-based recognition of human motion intention, dynamics modeling and identification of a lower limb rehabilitation robot named iLeg is investigated. Due to the relatively strong motion constraints, the traditional identification methods become insufficient for iLeg in three aspects: 1) the coupling factors among joints have not been considered in the traditional joint friction models, which makes the structural error and the torque estimation errors relatively large; 2) because of the small and complicated feasible region caused by the motion constraints, the traditional initialization strategy, for searching the valid initial solutions of the optimization problem for the exciting trajectories, becomes very inefficient; and 3) the condition number of the observation matrix, calculated from the preliminary dynamic model and the associated optimized exciting trajectory, is too large for the identification, and, however, further reduction of the condition number has not been considered in the literature. Therefore, corresponding contributions are presented to overcome the limitation. First, the coupling factors among joints are considered in the joint friction model by using the Palmgren empirical formulation and a polynomial fitting method. Then, an indirectly generating strategy is designed, by which the valid initial solutions of the optimization problem can be found with good efficiency. Moreover, a recursive optimization method based on the optimization of the dynamic model and the exciting trajectories, is proposed to further reduce the condition number. Finally, the performance of the proposed methods is demonstrated by several experiments.

Generic Multiuser Coordinated Beamforming for Underlay Spectrum Sharing

The beamforming techniques have been recently studied as possible enablers for underlay spectrum sharing. The existing beamforming techniques have several common limitations: they are usually system model specific, cannot operate with arbitrary number of transmit/receive antennas, and cannot serve arbitrary number of users. Moreover, the beamforming techniques for underlay spectrum sharing do not consider the interference originating from the incumbent primary system. This paper extends the common underlay sharing model by incorporating the interference originating from the incumbent system into generic combined beamforming design that can be applied on interference, broadcast, or multiple access channels. This paper proposes two novel multiuser beamforming algorithms for user fairness and sum rate maximization, utilizing newly derived convex optimization problems for transmit and receive beamformers calculation in a recursive optimization. Both beamforming algorithms provide efficient operation for the interference, broadcast, and multiple access channels, as well as for arbitrary number of antennas and secondary users in the system. Furthermore, this paper proposes a successive transmit/receive optimization approach that reduces the computational complexity of the proposed recursive algorithms. The results show that the proposed complexity reduction significantly improves the convergence rates and can facilitate their operation in scenarios, which require agile beamformer computation.

EFFECTIVE COVERAGE AND CONNECTIVITY CONSERVATION WITH LOAD BALANCING FOR WSN

Wireless sensor networks provide maximum coverage area in a network as much as possible, as the basic objective. Such as, identifying the location of interruptions in combat zone and tracking of an object, with reliable services. Organization of sensor nodes to construct maximum subgroups with energy limit, ability to monitor every required discrete points and activation in alternate manner is the best possible method for quality assurance. Behind the objective accomplishing the maximum subgroups, in the aim of obtaining the maximum connectivity arises the question on assurance of connectivity among nodes. To assure full coverage with base station connectivity in each sensing node, this paper proposes a new algorithm as Maximum Connected Load Balancing Cover Tree (MCLCT) with dynamically formation of routing cover tress with load-balancing. This kind of problem can be known as maximum cover tree problem, proved as nondeterministic polynomial-complete. There are two techniques in proposed MCLCT, first one is conservation of coverage by using recursive heuristic coverage optimization, and second is strat egy for identification of route using probabilistic load balance. The proposed MCLCT provides the solution by sharing the load among the nodes while sensing and transmitting, hence this makes energy consumption balanced between the nodes. Collection of simulation results depicts that, the proposed method accomplishes the objectives in terms of conservation of connectivity and energy efficiency.

Delay-range-dependent synchronization of drive and response systems under input delay and saturation

This paper addresses the synchronization of nonlinear drive and response systems under input saturation and subject to input time-delay. In considering generalized forms of the systems, their dynamics are assumed to satisfy the one-sided Lipschitz condition along with the quadratic inner-boundedness rather than the conventional Lipschitz condition. Further, the time-delays are handled by application of the delay-range-dependent methodology, rather than the delay-dependent one, utilizable for both short and long time-delays. Synchronization controller designs are provided by application of the Lyapunov–Krasovskii functional, local sector condition, generalized Lipschitz continuity, quadratic inner-boundedness criterion and Jensen's inequality. To the best of the authors’ knowledge, a delay-range-dependent synchronization control approach for the one-sided Lipscitz nonlinear systems under input delay and saturation constraints is studied for the first time. A convex-routine-based solution to the controller gain formulation by application of recursive nonlinear optimization using cone complementary linearization is also provided. The proposed methodology is validated for synchronization of modified Chua's circuits under disturbances by considering the input delay and saturation constraints.

Performance Analysis and Optimization of Distributed Workflows in Heterogeneous Network Environments

Large-scale e-science features complex DAG-structured workflows comprised of computing modules with intricate inter-module dependencies. Mapping such workflows in heterogeneous network environments and optimizing their end-to-end performance are crucial to the success of scientific collaborations that require fast system response and smooth data flow. We construct analytical cost models and formulate workflow mapping as optimization problems for minimum end-to-end delay and maximum frame rate. The difficulty of these problems essentially arises from the topological matching nature in the spatial domain, which is further compounded by the resource sharing complicacy in the temporal dimension. For unitary processing applications, we develop a workflow mapping algorithm based on a recursive critical path optimization procedure to minimize the latency; while for streaming applications, we conduct a rigorous workflow stability analysis and develop a layer-oriented dynamic programming solution based on topological sorting to identify and minimize the global bottleneck time. The accuracy of the proposed exact delay calculation algorithm is verified in comparison with an approximate solution, a dynamic distributed system simulation program, and a real network deployment, and the performance superiority of the proposed mapping approaches are illustrated by extensive simulation-based comparisons with existing algorithms and verified by large-scale experiments on real-life scientific workflows through effective system implementation and deployment in real networks.

Costless Delay in Negotiations

We study strategic negotiation models featuring costless delay, general recognition procedures, endogenous voting orders, and finite sets of alternatives. Two examples show: 1. non-existence of stationary subgame-perfect equilibrium (SSPE). 2. the recursive equations and optimality conditions are necessary for SSPE but insufficient because these equations can be singular. Strategy profiles excluding perpetual disagreement guarantee non-singularity. The necessary and sufficient conditions for existence of stationary best responses additionally require either an equalizing condition or a minimality condition. Quasi SSPE only satisfy the recursive equations and optimality conditions. These always exist and are SSPE if either all equalizing conditions or all minimality conditions hold.