Necessary conditions for continuous parameter stochastic optimization problems.
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Kushner, H. J.↗
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Results for “Continuous optimization”
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Foundations of aeroelastic optimization and some applications to continuous systems
Static and dynamic aeroelastic problems in optimization of continuous systems
Armand, J.-L.↗
Aerostructural Weight Estimation for a Transonic Truss-Braced Wing using the Higher-fidelity Conceptual Design and Structural Optimization Tool
Continued development and enhancements of the Higher-fidelity Conceptual Design and structural optimization (HCDstruct) tool has been driven largely by advanced aircraft concepts of interest to NASA. While previous versions of HCDstruct were limited to hybrid wing body (HWB) and generalized tube and wing (TW) aircraft concepts, the latest version of HCDstruct supports the analysis of Truss-Braced Wing (TBW) aircraft concepts, where users can model both high and low wing configurations as well as strut and jury geometries parametrically. Additionally, new methods for modeling advanced composite materials within HCDstruct have been implemented. These recent tool enhancements were demonstrated for an independent assessment of the NASA/Boeing SUGAR Phase VI Mach 0.8 Transonic Truss-Braced Wing (TTBW) concept.
Zachary D. Windous↗
Optimal design of compact spur gear reductions
The optimal design of compact spur gear reductions includes the selection of bearing and shaft proportions in addition to gear mesh parameters. Designs for single mesh spur gear reductions are based on optimization of system life, system volume, and system weight including gears, support shafts, and the four bearings. The overall optimization allows component properties to interact, yielding the best composite design. A modified feasible directions search algorithm directs the optimization through a continuous design space. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for optimization. After finding the continuous optimum, the designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearings on the optimal configurations.
Savage, M.↗
Stability Analysis of Streaks Induced by Optimized Vortex Generators
Numerical computations are performed to investigate the potential for transition control in an axisymmetric boundary layer via fully realizable, streamwise stationary streaks induced by an azimuthally periodic array of surface mounted vortex generators (VGs). Previous work has shown that suitable streaks of this type can significantly reduce the growth of Mack’s second mode instabilities, but large streak amplitudes can make the flow susceptible to previously absent streak instabilities that can become the leading cause of transition. Here, we use the adjoint capabilities of the SU2 flow solver to optimize the VG shape to maximize the reduction in the growth of second-mode disturbances while also preventing the streak amplitudes from reaching large enough values to precipitate an earlier onset of transition via streak instabilities. The geometry and the freestream flow conditions are selected to match a relevant trajectory lo-cation from the HIFiRE-1 flight experiment. Results show that the optimized VGs can increase the mean streak amplitude by 117% with respect to a manually developed baseline design. The stability of this optimized basic state is analyzed via the plane-marching parabolized stability equations, predicting a fully laminar flow over the entire cone, or equivalently, yielding transition delay of 130% versus the 17% for the baseline VGs.
Boundary layer transition↗
Nonsmooth trajectory optimization - An approach using continuous simulated annealing
An account is given of the properties of a continuous simulated annealing algorithm that can function as a global optimization tool for nonsmooth dynamic systems, as shown in the case of a trajectory-optimization program implementation. The approach is shown to successfully solve the problem of nonsmooth trajectory optimization for a high performance rigid-body aircraft. The results obtained demonstrate the superiority of the simulated annealing algorithm over widely used algorithms.
Lu, Ping↗
Multiplier-continuation algorthms for constrained optimization
Several path following algorithms based on the combination of three smooth penalty functions, the quadratic penalty for equality constraints and the quadratic loss and log barrier for inequality constraints, their modern counterparts, augmented Lagrangian or multiplier methods, sequential quadratic programming, and predictor-corrector continuation are described. In the first phase of this methodology, one minimizes the unconstrained or linearly constrained penalty function or augmented Lagrangian. A homotopy path generated from the functions is then followed to optimality using efficient predictor-corrector continuation methods. The continuation steps are asymptotic to those taken by sequential quadratic programming which can be used in the final steps. Numerical test results show the method to be efficient, robust, and a competitive alternative to sequential quadratic programming.
Lundberg, Bruce N.↗
Diagnostic yield and optimal duration of continuous-loop event monitoring for the diagnosis of palpitations. A cost-effectiveness analysis
BACKGROUND: Continuous-loop event recorders are widely used for the evaluation of palpitations, but the optimal duration of monitoring is unknown. OBJECTIVE: To determine the yield, timing, and incremental cost-effectiveness of each week of event monitoring for palpitations. DESIGN: Prospective cohort study. PATIENTS: 105 consecutive outpatients referred for the placement of a continuous-loop event recorder for the evaluation of palpitations. MEASUREMENTS: Diagnostic yield, incremental cost, and cost-effectiveness for each week of monitoring. RESULTS: The diagnostic yield of continuous-loop event recorders was 1.04 diagnoses per patient in week 1, 0.15 diagnoses per patient in week 2, and 0.01 diagnoses per patient in week 3 and beyond. Over time, the cost-effectiveness ratio increased from $98 per new diagnosis in week 1 to $576 per new diagnosis in week 2 and $5832 per new diagnosis in week 3. CONCLUSIONS: In patients referred for evaluation of palpitations, the diagnostic yield of continuous-loop event recording decreases rapidly after 2 weeks of monitoring. A 2-week monitoring period is reasonably cost-effective for most patients and should be the standard period for continuous-loop event recording for the evaluation of palpitations.
NASA Discipline Cardiopulmonary↗
An optimal terminal guidance method for continuous powered space vehicles.
Error correcting problem in space trajectory of continuous powered space vehicle, discussing optimal terminal guidance
OPTIMAL CONTROL↗
Locally optimal-digital redesign of continuous-time systems
This paper presents a new optimal digital redesign technique for finding a dynamic digital control law from the given continuous-time counterpart by minimizing a local quadratic performance index. The quadratic performance index is chosen as the integral of the weighted squared difference between the states of the original closed-loop system and those of the digitally controlled closed-loop system at any instant between each sampling period. The developed optimal digital redesign control law enables the states of the digitally controlled closed-loop system 10 closely match those of the original closed-loop system at any instant between each sampling period, and it can easily be implemented using microcomputers with a relatively large sampling period.
Shieh, Leang-San↗
Optimal digital redesign of continuous-time controllers
This paper proposes a new optimal digital redesign technique for finding a dynamic digital control law from the available analog counterpart and simultaneously minimizing a quadratic performance index. The proposed technique can be applied to a system with a more general class of reference inputs, and the developed digital regulator can be implemented using low cost microcomputers.
Shieh, Leang S.↗
Accelerating Continuous Variable Coherent Ising Machines Via Momentum
The Coherent Ising Machine (CIM) is a non-conventional architecture that takes inspiration from physical annealing processes to solve Ising problems heuristically. Its dynamics are naturally continuous and described by a set of ordinary differential equations that have been proven to be useful for the optimization of continuous variables nonconvex quadratic optimization problems. The dynamics of such Continuous Variable CIMs (CV-CIM) encourage optimization via optical pulses whose amplitudes are determined by the negative gradient of the objective; however, standard gradient descent is known to be trapped by local minima and hampered by poor problem conditioning. In this work, we propose to modify the CV-CIM dynamics using more sophisticated pulse injections based on tried-and-true optimization techniques such as momentum and Adam. Through numerical experiments, we show that the momentum and Adam updates can significantly speed up the CV-CIM’s convergence and improve sample diversity over the original CV-CIM dynamics. We also find that the Adam-CV-CIM’s performance is more stable as a function of feedback strength, especially on poorly conditioned instances, resulting in an algorithm that is more robust, reliable, and easily tunable. More broadly, we identify the CIM dynamical framework as a fertile opportunity for exploring the intersection of classical optimization and modern analog computing.
Ising Model↗
On optimal nonlinear estimation. I - Continuous observation.
A generalization of Bucy's (1965) representation theorem is obtained under very weak hypotheses. The generalized theorem is shown to play the same role in the case of general optimal estimation for an arbitrary random process as does the Bucy theorem in the case of optimal filtering for a diffusion process. At least for the models considered, the possibility is pointed out to reduce all sequential estimation problems to the problem of filtering. Hence, filtering theory is seen to represent the core of estimation theory, and is believed to define the direction in which future research should be focused.
Lo, J. T.↗
A Bell-Curved Based Algorithm for Mixed Continuous and Discrete Structural Optimization
An evolutionary based strategy utilizing two normal distributions to generate children is developed to solve mixed integer nonlinear programming problems. This Bell-Curve Based (BCB) evolutionary algorithm is similar in spirit to (mu + mu) evolutionary strategies and evolutionary programs but with fewer parameters to adjust and no mechanism for self adaptation. First, a new version of BCB to solve purely discrete optimization problems is described and its performance tested against a tabu search code for an actuator placement problem. Next, the performance of a combined version of discrete and continuous BCB is tested on 2-dimensional shape problems and on a minimum weight hub design problem. In the latter case the discrete portion is the choice of the underlying beam shape (I, triangular, circular, rectangular, or U).
Kincaid, Rex K.↗
Modularized ion thruster development
A family of mercury ion thruster modules has been developed which extends the basic design of the Hughes-developed 1-mlb Engineering Model Thruster to accommodate the extended thrust range from 0.5 mlb to 4 mlb. In the subject program, separate Discharge Chamber Modules (DCM's) have been optimized for operation at nominal thrust levels T = 0.5 mlb and 2 mlb; DCM optimization is continuing at thrust level T = 4 mlb. Performance optimization required modification of the beam-extraction system and of discharge-chamber components; however, the cathodes and mechanical structure are unchanged from the Engineering Model design. Performance data on the optimized modules are given.
Hyman, J., Jr.↗
Continuation methods in multiobjective optimization for combined structure control design
A homotopy approach involving multiobjective functions is developed to outline the methods that have evolved for the combined control-structure optimization of physical systems encountered in the technology of large space structures. A method to effect a timely consideration of the control performance prior to the finalization of the structural design involves integrating the control and structural design processes into a unified design methodology that combines the two optimization problems into a single formulation. This study uses the combined optimization problem as a family of weighted structural and control costs. Connections with vector optimizations are described; an analysis of the zero-set of required conditions is made, and a numerical example is given.
Milman, M.↗
Data Optimization for the Cloud, Continued: Earthdata Cloud Services
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Patrick Quinn↗
Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing
A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.
Childs, A. G.↗