Matrix analysis
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Mathematical control theory: an introduction
Mathematical control theory: an introduction
Discrete-time control systems (2nd ed.)
Discrete-time control systems (2nd ed.)
Robust and optimal control
Mathematical control theory
Optimal control, geometry, and mechanics
Mathematical control theory
Optimal control, optimization, and analytical mechanics
Mathematical control theory
Multiobjective control for robot telemanipulators
Advances in linear matrix inequality methods in control
Trust-region methods
Practical methods for optimal control using nonlinear programming
Practical methods for optimal control using nonlinear programming
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Modern Control Engineering
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Semidefinite Programming vs. LP Relaxations for Polynomial Programming
Mathematics of Operations Research
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
ACM Transactions on Mathematical Software (TOMS)
Introduction to Shape Optimization: Theory, Approximation, and Computation
Introduction to Shape Optimization: Theory, Approximation, and Computation
Convex Optimization
Semidefinite Approximations for Global Unconstrained Polynomial Optimization
SIAM Journal on Optimization
Sum of Squares Approximation of Polynomials, Nonnegative on a Real Algebraic Set
SIAM Journal on Optimization
A Sum of Squares Approximation of Nonnegative Polynomials
SIAM Journal on Optimization
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We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.