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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Nonlinear Optimal Control of Electron Dynamics Within Hartree-Fock Theory

Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of motion—the time-dependent Schrödinger equation (TDSE)—is numerically intractable. Here, we present a solution of this problem within time-dependent Hartree-Fock (TDHF) theory, a mean field approximation of the TDSE. Optimality is defined in terms of minimizing the total control effort while maximizing the overlap between desired and achieved target states. We frame this problem as an optimization problem constrained by the nonlinear TDHF equations; we solve it using trust region optimization with gradients computed via a custom-built adjoint state method. For three molecular systems, we show that with very small neural network parametrizations of the control, our method yields solutions that achieve desired targets within acceptable constraints and tolerances.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Numerical experience with a class of algorithms for nonlinear optimization using inexact function and gradient information

For optimization problems associated with engineering design, parameter estimation, image reconstruction, and other optimization/simulation applications, low accuracy function and gradient values are frequently much less expensive to obtain than high accuracy values. Here, researchers investigate the computational performance of trust region methods for nonlinear optimization when high accuracy evaluations are unavailable or prohibitively expensive, and confirm earlier theoretical predictions when the algorithm is convergent even with relative gradient errors of 0.5 or more. The proper choice of the amount of accuracy to use in function and gradient evaluations can result in orders-of-magnitude savings in computational cost.

Carter, Richard G.↗
NASA NTRS2010

Exhaustive Versus Randomized Searchers for Nonlinear Optimization in 21st Century Computing: Solar Application

We present a simple multi-dimensional exhaustive search method to obtain, in a reasonable time, the optimal solution of a nonlinear programming problem. It is more relevant in the present day non-mainframe computing scenario where an estimated 95% computing resources remains unutilized and computing speed touches petaflops. While the processor speed is doubling every 18 months, the band width is doubling every 12 months, and the hard disk space is doubling every 9 months. A randomized search algorithm or, equivalently, an evolutionary search method is often used instead of an exhaustive search algorithm. The reason is that a randomized approach is usually polynomial-time, i.e., fast while an exhaustive search method is exponential-time i.e., slow. We discuss the increasing importance of exhaustive search in optimization with the steady increase of computing power for solving many real-world problems of reasonable size. We also discuss the computational error and complexity of the search algorithm focusing on the fact that no measuring device can usually measure a quantity with an accuracy greater than 0.005%. We stress the fact that the quality of solution of the exhaustive search - a deterministic method - is better than that of randomized search. In 21 st century computing environment, exhaustive search cannot be left aside as an untouchable and it is not always exponential. We also describe a possible application of these algorithms in improving the efficiency of solar cells - a real hot topic - in the current energy crisis. These algorithms could be excellent tools in the hands of experimentalists and could save not only large amount of time needed for experiments but also could validate the theory against experimental results fast.

Sen, Syamal K.↗
NASA NTRS1987

A method for nonlinear optimization with discrete design variables

A numerical method is presented for the solution of nonlinear discrete optimization problems. The applicability of discrete optimization to engineering design is discussed, and several standard structural optimization problems are solved using discrete design variables. The method uses approximation techniques to create subproblems suitable for linear mixed-integer programming methods. The method employs existing software for continuous optimization and integer programming.

Olsen, Gregory R.↗
NASA NTRS2012

Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems

In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.

planetary soft landing↗
NASA NTRS1998

On Managing the Use of Surrogates in General Nonlinear Optimization and MDO

This paper is concerned with a trust region approximation management framework (AMF) for solving the nonlinear programming problem in general and multidisciplinary optimization problems in particular The intent of the AMF methodology is to facilitate the solution of optimization problems with high-fidelity models. While such models are designed to approximate the physical phenomena they describe to a high degree of accuracy, their use in a repetitive procedure, for example, iterations of an optimization or a search algorithm, make such use prohibitively expensive. An improvement in design with lower-fidelity, cheaper models, however, does not guarantee a corresponding improvement for the higher-fidelity problem. The AMF methodology proposed here is based on a class of multilevel methods for constrained optimization and is designed to manage the use of variable-fidelity approximations or models in a systematic way that assures convergence to critical points of the original high-fidelity problem.

Alexandrov, Natalia M.↗
NASA NTRS1990

Global nonlinear optimization of spacecraft protective structures design

The global optimization of protective structural designs for spacecraft subject to hypervelocity meteoroid and space debris impacts is presented. This nonlinear problem is first formulated for weight minimization of the space station core module configuration using the Nysmith impact predictor. Next, the equivalence and uniqueness of local and global optima is shown using properties of convexity. This analysis results in a new feasibility condition for this problem. The solution existence is then shown, followed by a comparison of optimization techniques. Finally, a sensitivity analysis is presented to determine the effects of variations in the systemic parameters on optimal design. The results show that global optimization of this problem is unique and may be achieved by a number of methods, provided the feasibility condition is satisfied. Furthermore, module structural design thicknesses and weight increase with increasing projectile velocity and diameter and decrease with increasing separation between bumper and wall for the Nysmith predictor.

Mog, R. A.↗
NASA NTRS1973

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.↗
NASA NTRS1994

Optimal nonlinear estimation for aircraft flight control in wind shear

The most recent results in an ongoing research effort at Princeton in the area of flight dynamics in wind shear are described. The first undertaking in this project was a trajectory optimization study. The flight path of a medium-haul twin-jet transport aircraft was optimized during microburst encounters on final approach. The assumed goal was to track a reference climb rate during an aborted landing, subject to a minimum airspeed constraint. The results demonstrated that the energy loss through the microburst significantly affected the qualitative nature of the optimal flight path. In microbursts of light to moderate strength, the aircraft was able to track the reference climb rate successfully. In severe microbursts, the minimum airspeed constraint in the optimization forced the aircraft to settle on a climb rate smaller than the target. A tradeoff was forced between the objectives of flight path tracking and stall prevention.

Mulgund, Sandeep S.↗
NASA NTRS1972

Adaptive nonlinear optimization of the signal-to-noise ratio of an array subject to a constraint.

Investigation of a stochastic projected gradient algorithm which can be used to find a constrained optimum point for a concave or convex objective function subject to nonlinear constraints. When the constraint consists of only one linear equation, convergence to the constrained optimum value is proven, and bounds are obtained for the rate of convergence of the algorithm to the constrained optimum value. This algorithm is then applied to the nonlinear problem of automatically making an array of detectors form a beam in a desired direction in space when unknown interfering noise is present so as to maximize the signal-to-noise ratio subject to a constraint on the supergain ratio.

Winkler, L. P.↗
NASA NTRS2003

Route Monopolie and Optimal Nonlinear Pricing

To cope with air traffic growth and congested airports, two solutions are apparent on the supply side: 1) use larger aircraft in the hub and spoke system; or 2) develop new routes through secondary airports. An enlarged route system through secondary airports may increase the proportion of route monopolies in the air transport market.The monopoly optimal non linear pricing policy is well known in the case of one dimension (one instrument, one characteristic) but not in the case of several dimensions. This paper explores the robustness of the one dimensional screening model with respect to increasing the number of instruments and the number of characteristics. The objective of this paper is then to link and fill the gap in both literatures. One of the merits of the screening model has been to show that a great varieD" of economic questions (non linear pricing, product line choice, auction design, income taxation, regulation...) could be handled within the same framework.VCe study a case of non linear pricing (2 instruments (2 routes on which the airline pro_ddes customers with services), 2 characteristics (demand of services on these routes) and two values per characteristic (low and high demand of services on these routes)) and we show that none of the conclusions of the one dimensional analysis remain valid. In particular, upward incentive compatibility constraint may be binding at the optimum. As a consequence, they may be distortion at the top of the distribution. In addition to this, we show that the optimal solution often requires a kind of form of bundling, we explain explicitly distortions and show that it is sometimes optimal for the monopolist to only produce one good (instead of two) or to exclude some buyers from the market. Actually, this means that the monopolist cannot fully apply his monopoly power and is better off selling both goods independently.We then define all the possible solutions in the case of a quadratic cost function for a uniform distribution of agent types and explain the implications for airlines in terms of service differentiation.

Tournut, Jacques↗
NASA NTRS1989

A penalty approach for nonlinear optimization with discrete design variables

Introduced here is a simple approach to minimization problems with discrete design variables by modifying the penaly function approach of converting the constrained problems into sequential unconstrained minimization technique (SUMT) problems. It was discovered, during the course of the present work, that a similar idea was suggested by Marcal and Gellatly. However, no further work has been encountered. A brief description of the SUMT is presented. The form of the penalty function for the discrete-valued design variables and strategy used for the implementation of the procedure is discussed next. Finally, several design examples are used to demonstrate the procedure, and results are compared with the ones available in the literature.

Shin, Dong K.↗