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An algorithm for noisy function minimization for use in determining optimal trajectories

I. Bert Russak

An algorithm for noisy function minimization for use in determining optimal trajectories

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  • 2 Currently reading

Published by Naval Postgraduate School in Monterey, California .
Written in English

  • Trajectory optimization,
  • Ballistic missile defenses

  • About the Edition

    This work concerns a technique to be used in the solution of optimal trajectory problems associated with kinetic energy weapons. In this problem, it is desired to solve for a control function (which might be thrust magnitude and direction of gimbaled engine) in time in order to minimize time to intercept an enemy missile. Such problems are really infinite dimensional in nature (i.e., determining the control at each time point along the trajectory). However, in using a digital computer to solve such problems, certain operations occur which make the problem discrete and so viewable in a finite dimensional setting. For example, to numerically integrate the differential equations of motion, only values of thrust at a finite number of time points (typically, the beginning of each integration interval) affect the trajectory. The problem then is to determine these values so as to minimize the time to intercept. For any particular trajectory, this quantity is computed through a complicated flight equation simulation model. Also inherent in this computation is noise so that the computed time to intercept is really a noisy quantity. The current algorithm considers the noise in solving for the optimal control.

    Edition Notes

    Statementby I.B. Russak, J.B. Bassingthwaighte, I.S. Chan [and] A.A. Goldstein
    ContributionsBassingthwaighte, J. B., Chan, I. S., Goldstein, A. A., Naval Postgraduate School (U.S.)
    The Physical Object
    Pagination8 p. :
    ID Numbers
    Open LibraryOL25499285M

    of the proximal point algorithm for the quasiconvex case it is needed to solve the iteration () using a local optimization algorithm, which only provides an approximate solution. Thus it is important to consider inexact methods. Therefore, from the computational point of view, is it possible to introduce a inexact proximal method to solve (1 Cited by: Overview. The goal of a branch-and-bound algorithm is to find a value x that maximizes or minimizes the value of a real-valued function f(x), called an objective function, among some set S of admissible, or candidate set S is called the search space, or feasible rest of this section assumes that minimization of f(x) is desired; this assumption comes without loss of.   The elite individual represents the suitable solution of the population using an elitism strategy to produce a faster convergence of the algorithm to the optimal solution of the problem. The use of elitist individual guarantees that the best fitness individual never increases (minimization problem) from one iteration to the next iteration. Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. Mathematical optimization on a noisy function. Ask Question Asked 5 years, 1 month ago. Active 5 years, 1 month ago. I want to use my course material to write a book in the future.

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An algorithm for noisy function minimization for use in determining optimal trajectories by I. Bert Russak Download PDF EPUB FB2

TITLE (and Sublllla) An Algorithm For Noisy Function Minimization For Use In Determining Optimal Trajectories». TYPE Of REPORT 4 PERIOD COVEREO Technical Report. Academic Year 4 PIRFORMINO ORO. An algorithm for noisy function minimization for use in determining optimal trajectories.

By J. Bassingthwaighte, I. Chan, A. Goldstein and I. Bert Russak. Download PDF ( KB) Abstract. This work concerns a technique to be used in the solution of optimal trajectory problems associated with kinetic energy weapons. () Benefits of noise in M-estimators: Optimal noise level and probability density.

Physica A: Statistical Mechanics and its Applications() Sound- and current-driven laminar profiles and their application method mimicking acoustic responses in Cited by: The algorithm explores the entire domain and proceeds to determine potentially good subregions for future investigation.

2 Phase II is a local exploitation step. Local optimization algorithms are applied to determine the nal solution. 0 1 2 0 1 2 0 1File Size: KB. On optimization of algorithms for function minimization 49 The computation ofa(K) is m general difficult, a relatively good approximation ofa(K) is given by g (K) the centre if gravity of K.

g (K) can be computed by dividing K into Simplexes Kj, i = l, 2, 5, computing g (.) - which is the vertorial (arithmetical) mean of the vertices of A",-then gw= (L^^) &^^Author: G.

Sonnevend. 3) the proximity of the optimal policy’s feature distribution to the convex hull of the training data. This provides a use-ful a posteriori bound since all but the expert scoring noise are easily calculated after the algorithm is run.

We could use L 1regression to couple the regression perfectly with the analysis. () An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications. Mathematical Programming() Superrelaxation and the rate of convergence in minimizing quadratic functions subject to bound by: Optimal trajectories f An algorithm for noisy function minimization for use in determining optimal trajectories book time-critical.

determining the optimal final state An algorithm for noisy function minimization for use in determining optimal trajectories book of an optimal function class.

such as in Theo-rems 1 and 2. A nice chapter on function optimization techniques: Numerical Recipes in C, chapter 10 (2nd or 3rd edition, 2nd edition is electronically available for free under Obsolete Versions): Minimization or Maximization of Functions, This material from any other numerical methods book is also fine.

Koyuncu et al.,). Instead of using an explicit representation of the environment, sampling-based algorithms rely on a collision checking module, providing information about feasibility of candidate trajectories, and connect a set of points sampled from the obstacle-free space in order to build a graph (roadmap) of feasible trajectories.

The application of a hybrid memetic constrained minimization algorithm that uses the ideas of evolutionary methods operating the concept of population and the algorithms of simulation and mutual learning of the population’s individuals for designing the optimal control of bunches of trajectories of nonlinear deterministic systems with incomplete Cited by: 5.

The discrete L-curve method is popular for determining the value of An algorithm for noisy function minimization for use in determining optimal trajectories book regularization parameter in the iterative regularization methods where a compromise is made between the minimization of the.

An Improved Algorithm for the L 2 LpMinimization Problem 3 complexity O(32), whereas a higher computational complexity is required at each iteration.

Bian et al. [2] present an smoothing quadratic regularization al-gorithm for solving a class of unconstrained non-smooth non-convex problems. Nonlinear Optimization for Optimal Control Pieter Abbeel UC Berkeley EECS Many slides and figures adapted from Stephen Boyd [optional] Boyd and Vandenberghe, Convex Optimization, Chapters 9 – 11 [optional] Betts, Practical Methods for Optimal Control Using.

Rojas: Neural Networks, Springer-Verlag, Berlin, 7 The Backpropagation Algorithm Learning as gradient descent We saw in the last chapter that multilayered networks are capable of com-File Size: 2MB.

The objective function for the optimization was a minimization of MTOW. The use of genetic real coded algorithm (GA) as an optimization tool for an aircraft can help to reduce the number of qualitative decisions.

Also, using GA approach, the time and the cost Cited by: 6. Mathematical optimization: finding minima of functions. Authors: Gaël Varoquaux. Mathematical optimization deals with the problem of finding numerically minimums (or maximums or zeros) of a function.

In this context, the function is called cost function, or objective function, or energy. Here, we are interested in using ze for black-box optimization: we do not rely on the. LEARNING OPTIMAL NONLINEARITIES FOR ISTA 1 Learning optimal nonlinearities for iterative thresholding algorithms Ulugbek S.

Kamilov, Member, IEEE and Hassan Mansour, Member, IEEE Abstract—Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems.

Convex Optimization — Boyd & Vandenberghe Unconstrained minimization • terminology and assumptions • gradient descent method • we assume optimal value p • clearly shows two phases in algorithm Unconstrained minimization 10–File Size: KB. This example shows how to create and minimize a fitness function for the genetic algorithm solver ga using three techniques: The basic fitness function is Rosenbrock's function, a common test function for optimizers.

The function is a sum of squares: f (x) = 1 0 0 (x 1 2 - x 2) 2 + (1 - x 1) 2. The function has a minimum value of zero at the. Stochastic optimization is used with random (noisy) function measurements or random inputs in the search process.

Infinite-dimensional optimization studies the case when the set of feasible solutions is a subset of an infinite-dimensional space, such as a space of functions.

Lecture 26 Outline • Necessary Optimality Conditions for Constrained Problems • Karush-Kuhn-Tucker∗ (KKT) optimality conditions Equality constrained problems Inequality and equality constrained problems • Convex Inequality Constrained Problems Sufficient optimality conditions • The material is in Chapter 18 of the book • Section • Lagrangian Method in Section (see 18 File Size: KB.

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 40, NO.9, SEPTEMBER Efficient Algorithms for Globally Optimal Trajectories John N. Tsitsiklis, Member, IEEE Abstract-We present serial and parallel algorithms for solving a system of equations that arises from the discretization of the Hamilton-Jacobi equation associated to a trajectory optimization.

middle point discrete simultaneous perturbation stochastic approximation (DSPSA) algorithm for the stochastic optimization of a loss function defined ona p-dimensional grid of points in Euclidean space. We show that the sequence generated by DSPSA converges to the optimal point under some by: 6.

The estimate holds provided the system have time-optimal controls with bounded variation. This estimate is of order v with respect to the discretization step in time, if the minimal time function is Hölder continuous of exponent v.

The proof combines the convergence result obtained in [2] by PDE methods, with direct control-theoretic by: * The optimal shapes are not computed in the context of PDE’s but rather for suitable numerical approximations.

Even in those cases in which an optimal shape is known to exist and in which one is able to write a reasonable descent algorithm, it has to be. In statistics, an expectation–maximization (EM) algorithm is an iterative method to find maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using.

The MM algorithm is an iterative optimization method which exploits the convexity of a function in order to find their maxima or minima.

The MM stands for “Majorize-Minimization” or “Minorize-Maximization”, depending on whether the desired optimization is a maximization or a minimization. Gradient descent is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. To find a local minimum of a function using gradient descent, we take steps proportional to the negative of the gradient (or approximate gradient) of the function at the current point.

But if we instead take steps proportional to the positive of the gradient, we approach. LogitBoost (algorithm ) is an algorithm also derived using Newton’s method, but applied to the logistic loss.

As in exerciseassume all of the base functions in are classifiers. An Analysis Dictionary Learning Algorithm under a Noisy Data Model with Orthogonality Constraint. By keeping Ω fixed, the optimal backward greedy algorithm (OBG) The convergence curves of the ADL algorithms for both the noise-free and noise case (where SNR = 25 dB).Cited by: 5.

Reinforcement learning (RL) is an area of machine learning concerned with how software agents ought to take actions in an environment in order to maximize the notion of cumulative reward.

Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning. Reinforcement learning differs from supervised learning in not needing.

In fact, the RRT algorithm almost always converges to a non-optimal solution. Second, it is shown that the probability of the same event for the RRG algorithm is one. That is, the RRG algorithm is asymptotically optimal, in the sense that it converges to an optimal solution almost surely as the number of samples approaches infinity.

C.M. Silva, E.C. Biscaia Jr., in Computer Aided Chemical Engineering, Penalty function method. A fuzzy penalty function method has been adopted to treat constrained multiobjective optimization problems. This method incorporates the constraints into the objective functions by using a transferred function, which carries information on the point's position and feasibility (Cheng and Li, ).

Consider the problem of finding a root of the multivariate gradient equation that arises in function minimization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general Kiefer-Wolfowitz type is appropriate for estimating the root.

An algorithm for synthesizing optimal aircraft trajectories for specified range has been developed and implemented in a computer program written in FORTRAN IV. This report describes the algorithm, its computer implementation, and a set of example optimum trajectories for the Boeing aircraft.

Machine Learning Gradient Descent Illustrated Srihari • 2Given function is f (x)=½ x which has a bowl shape with global minimum at x=0 – Since f ’(x)=x • For x>0, f(x) increases with x and f’(x)>0 • For xUse f’(x) to follow function downhill – Reduce f (x) by going in direction opposite sign of derivative f’(x)File Size: 1MB.

Continuation of Convex Optimization I. Subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound.

Robust optimization. Selected applications in areas such as control, circuit design. Training neural networks is by minimization a cost function defined using the output of the network and measurements from the modeled system (Zhang and Suganthan, ).

Classical training approaches use derivatives of the cost function to update the weights of the neural network (Gori and Tesi, ; Montingy, ). Unfortunately. Function Minimization Algorithms • Quine McClusky Method (Q-M Method, Tabular Method) • Use adjacency property, e.g., ab +ab’=a. • Iterated Consensus • Use consensus operation and absorption property, e.g., ab ¢ a’c =bc, a+ab =a.

• Prime Implicant Table •. Pdf the optimal pdf occurs at the boundary of the feasible region, the procedure moves from the interior to the boundary, hence interior-pointmethods. The barrier function approach was first proposed in the early sixties and later popularised and thoroughly investigated by Fiacco and McCormick.

Algorithms for convex optimization – p/33File Size: 1MB.The CE method was motivated by an adaptive algorithm for estimating probabilities of rare events in complex stochastic networks (Rubinstein, ), which involves variance minimization.

It was soon realized (Rubinstein,) that a simple cross-entropy modi cation of (Rubinstein, ) could be.Rapidly growing Global Ebook System (GPS) data plays an important role in ebook and their applications (e.g., GPS-enabled smart devices). In order to employ K-means to mine the better origins and destinations (OD) behind the GPS data and overcome its shortcomings including slowness of convergence, sensitivity to initial seeds selection, and getting stuck in a local optimum, this Cited by: 6.