Recent advances in gradient algorithms for optimal control problems

Applied Optimal Control

2018 • 5,869 citations

The Mathematical Theory of Optimal Processes

1965 • 3,275 citations

Numerical Methods for Two-Point Boundary Value Problems

2019 • 1,251 citations

Quasilinearization and nonlinear boundary value problems

1966 • 1,137 citations

Quasilinearization and nonlinear boundary-value problems

1965 • 994 citations

Calculus of Variations and Optimal Control Theory

1967 • 958 citations

Lectures on the calculus of variations

1946 • 862 citations

NUMERICAL METHODS FOR TWO-POINT BOUNDARY-VALUE PROBLEMS

1969 • 747 citations

Calculus of Variations and Optimal Control Theory

1967 • 528 citations

Two-Point Boundary Value Problems: Shooting Methods

1973 • 499 citations

Numerical Solution of Ordinary and Partial Differential Equations

1963 • 494 citations

A Steepest-Ascent Method for Solving Optimum Programming Problems

1962 • 476 citations

Gradient Theory of Optimal Flight Paths

1960 • 444 citations

The conjugate gradient method for optimal control problems

1967 • 406 citations

Nonlinear Two Point Boundary Value Problems

1968 • 361 citations

New necessary conditions of optimality for control problems with state-variable inequality constraints

1971 • 340 citations

OPTIMAL PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS

1963 • 298 citations

Introduction to Optimal Control

1970 • 295 citations

Optimization techniques

1963 • 285 citations

The Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations.

1959 • 269 citations

Variational methods in problems of control and programming

1961 • 234 citations

Optimization and Control of Nonlinear Systems Using the Second Variation

1963 • 223 citations

An introduction to optimal control

1967 • 205 citations

A transformation technique for optimal control problems with a state variable inequality constraint

1969 • 203 citations

Modern mathematics for the engineer

1957 • 183 citations

Sequential gradient-restoration algorithm for optimal control problems

1970 • 149 citations

Theory of optimum aerodynamic shapes

1965 • 145 citations

Optimal programming problems with inequality constraints. ii - solution by steepest-ascent

1964 • 142 citations

General technique for solving nonlinear, two-point boundary-value problems via the method of particular solutions

1970 • 113 citations

An interior penalty method for inequality constrained optimal control problems

1967 • 112 citations

The conjugate gradient method for optimal control problems with bounded control variables

1968 • 100 citations

Method of particular solutions for linear, two-point boundary-value problems

1968 • 97 citations

Sequential gradient-restoration algorithm for optimal control problems with nondifferential constraints

1974 • 88 citations

New second-order and first-order algorithms for determining optimal control: A differential dynamic programming approach

1968 • 86 citations

On control problems with bounded state variables

1962 • 85 citations

Contributions to the Calculus of Variations

1938 • 82 citations

First-order strong variation algorithms for optimal control

1975 • 76 citations

Optimization and Design

1974 • 70 citations

Comparison of several numerical optimization methods

1967 • 66 citations

Mathematics for Exterior Ballistics.

1944 • 61 citations

Davidon’s Method in Hilbert Space

1968 • 58 citations

A TRAJECTORY OPTIMIZATION TECHNIQUE BASED UPON THE THEORY OF THE SECOND VARIATION

1963 • 56 citations

The Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations.

1958 • 54 citations

The Numerical Integration of Two-Point Boundary Value Problems

1956 • 54 citations

Modified quasilinearization method for solving nonlinear, two-point boundary-value problems

1971 • 48 citations

The numerical integration of two-point boundary value problems

1956 • 47 citations

Rapid convergence to optimum solutions using a Min-H strategy.

1967 • 43 citations

Optimization using conjugate gradient methods

1970 • 39 citations

Conjugate direction methods for optimal control

1970 • 37 citations

First-order strong variation algorithms for optimal control problems with terminal inequality constraints

1975 • 37 citations

Modified quasilinearization algorithm for optimal control problems with nondifferential constraints

1974 • 34 citations

Newton-raphson operator - problems with undetermined end points

1965 • 33 citations

Solution of optimal control problems by the method of conjugate gradients

1967 • 32 citations

Modified quasilinearization and optimal initial choice of the multipliers part 2?Optimal control problems

1970 • 31 citations

Solution of two-point boundary-value problems with Jacobian matrix characterized by large positive Eigenvalues

1974 • 29 citations

The use of the adjoint variables in the development of improvement criteria for chemical reactors

1967 • 26 citations

Optimum Control, Inequality State Constraints, and the Generalized Newton-Raphson Algorithm

1965 • 25 citations

Modified quasilinearization and optimal initial choice of the multipliers part 1?Mathematical programming problems

1970 • 25 citations

On a new computing technique in optimal control and its application to minimal-time flight profile optimization

1969 • 24 citations

On a new computing technique in optimal control and its application to minimal time flight profile optimization

1970 • 24 citations

Summary and comparison of gradient-restoration algorithms for optimal control problems

1972 • 23 citations

On methods for obtaining solutions of fixed end-point problems in the calculus of variations

1953 • 21 citations

Extensions in quasilinearization techniques for optimal control

1968 • 19 citations

Balance function for the optimal control problem

1971 • 18 citations

Sequential conjugate-gradient-restoration algorithm for optimal control problems. Part 1. Theory

1975 • 17 citations

Numerical Solution of Nonlinear Equations and Nonlinear, Two-Point Boundary-Value Problems1 1This research, supported by the National Science Foundation under Grant No. GP-18522, is a condensation of the investigations described by Miele et al. (1, 2).

1971 • 16 citations

Second-order tests in optimization theories

1975 • 16 citations

Modified quasilinearization algorithm for optimal control problems with bounded state

1973 • 15 citations

Use of the method of particular solutions in nonlinear, two-point boundary-value problems

1968 • 15 citations

Second-variation methods in dynamic optimization

1969 • 15 citations

The restoration of constraints in holonomic and nonholonomic problems

1969 • 15 citations

Sequential conjugate-gradient-restoration algorithm for optimal control problems. Part 2. Examples

1975 • 14 citations

Multipoint approach to the two-point boundary value problem

1973 • 14 citations

Sequential gradient-restoration algorithm for optimal control problems with bounded state

1973 • 13 citations

Computational results for extensions in quasilinearization techniques for optimal control

1968 • 13 citations

A neighboring optimal feedback control scheme for systems using discontinuous control

1971 • 12 citations

Modifications and extensions of the sequential gradient-restoration algorithm for optimal control theory

1972 • 8 citations

Note on a problem by Lance and a problem by Bellman

1972 • 7 citations

Combined Gradient-Restoration Algorithm for Optimal Control Problems,

1971 • 7 citations

Gradient methods in control theory. Part 6 - Combined gradient-restoration algorithm

1970 • 6 citations

Numerical Solutions in the Simplest Problem of the Calculus of Variations

1972 • 5 citations

The Restoration of Constraints in Holonomic Problems

1968 • 5 citations

An extended quasilinearization algorithm

1973 • 5 citations

Modified Quasilinearization Method for Mathematical Programming Problems and Optimal Control Problems1 1This research, supported by the National Science Foundation under Grant No. GP-18522, is a condensation of the investigations described in Refs. 1–2.

1973 • 5 citations

Anchoring conditions for the sequential gradient-restoration algorithm and the modified quasilinearization algorithm for optimal control problems with bounded state

1973 • 4 citations

Method of Particular Solutions for Linear, Two-point Boundary-value Problems. Part 1 - Preliminary Examples

1968 • 4 citations

Solution of state-constrained optimal control problems through quasilinearization

1970 • 4 citations

Gradient methods in control theory. Part 5 - Sequential gradient-restoration algorithm, additional numerical examples

1970 • 4 citations

A modified perturbation method for solving optimal control problems with state variable inequality constraints

1971 • 3 citations

Sequential Gradient-Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints. Part 2. Examples,

1973 • 3 citations

Use of the method of particular solutions in nonlinear, two-point boundary-value problems. Part 1 - Uncontrolled systems

1968 • 3 citations

Method of particular solutions for linear, two point boundary value problems. Part 2 - General theory

1968 • 3 citations

A note on the gradient method

1972 • 3 citations

On the Miele-Iyer modified quasilinearization method

1974 • 3 citations

Gradient methods in control theory. Part 1 - Ordinary gradient method

1969 • 3 citations

A hybrid approach to optimal control problems with bounded state

1975 • 3 citations

Extremization of Terminally Constrained Control Problems

1972 • 2 citations

Use of the method of particular solutions in quasi-linearization.

1968 • 2 citations

Application of the method of particular solutions to boundary-layer analyses.

1968 • 2 citations

Variational Approach to the Gradient Method: Theory and Numerical Experiments

1969 • 2 citations

Deleted Work

1955 • 0 citations