Equivalent Nonlinear Programming Research Articles

Numerical direct kinematic analysis of fully parallel linearly actuated platform type manipulators

AbstractThis article presents a new numerical approach for solving the direct kinematics problem of fully parallel, linearly actuated platform manipulators. The solution procedure consists of two stages. The first stage transforms the direct kinematics problem into an equivalent nonlinear programming program, and a robust search algorithm is developed to bring the moving platform from arbitrary initial approximation to a feasible configuration that is near to the true solution. The second stage uses the Newton‐Raphson iterative method to converge the solution to the desired accuracy. This approach is numerically stable and computationally efficient. In addition, by randomly perturbing the initial approximations, it can be implemented successively to find multiple solutions to the direct kinematics problem. Two numerical examples are presented to demonstrate the stability and efficiency of this approach. © 2002 Wiley Periodicals, Inc.

Constrained stabilization problem and transient mismatch phenomenon in singularly perturbed systems

We initially study the control of linear systems by state feedback and simultaneously require the feedback gain matrix to satisfy a certain constraint equation. We provide two fundamentally different methods to solve the constrained stabilization problem. The first method parametrizes the class of stabilizing gain matrices and converts the problem to an equivalent nonlinear programming problem. The second method, on the other hand, converts the problem to an equivalent stabilization problem by a static output controller where the static gain is required to take a special structure. The motivation behind introducing this problem and its solution is the application of the results to the design of observer based controllers for the singularly perturbed systems. It is shown that the transient mismatch phenomenon, which occurs in this type of design, may be alleviated if the observer gain of the fast observer is chosen based on the solution of a certain constraint stabilization problem which involves the output matrix of the slow subsystem.

Neural network approach for allocation with capacity

In this paper we discuss neural network approach for allocation with capacity constraints problem. This problem can be formulated as zero-one integer programming problem. We transform this zero-one integer programming problem into an equivalent nonlinear programming problem by replacing zero-one constraints with quadratic concave equality constraints. We propose two kinds of neural network structures based on penalty function method and augmented Lagrangian multiplier method, and compare them by theoretical analysis and numerical simulation. We show that penalty function based neural network approach is not good to combinatorial optimization problem because it falls in the dilemma whether terminating at an infeasible solution or sticking at any feasible solution, and augmented Lagrangian multiplier method based neural network can alleviate this suffering in some degree.

A Massively Parallel Algorithm for Nonlinear Stochastic Network Problems

We develop an algorithm for solving nonlinear, two-stage stochastic problems with network recourse. The algorithm is based on the framework of row-action methods. The problem is formulated by replicating the first-stage variables and then adding nonanticipativity side constraints. A series of (independent) deterministic network problems are solved at each step of the algorithm, followed by an iterative step over the nonanticipativity constraints. The solution point of the iterates over the nonanticipativity constraints is obtained analytically. The row-action nature of the algorithm makes it suitable for parallel implementations. A data representation of the problem is developed that permits the massively parallel solution of all the scenario subproblems concurrently. The algorithm is implemented on a Connection Machine CM-2 with up to 32K processing elements and achieves computing rates of 276 MFLOPS. Very large problems—8,192 scenarios with a deterministic equivalent nonlinear program with 868,367 constraints and 2,474,017 variables—are solved within a few minutes. We report extensive numerical results regarding the effects of stochasticity on the efficiency of the algorithm.

A Cutting Plane Approach for Chance Constrained Linear Programs

One approach for solving linear programs with random coefficients is chance constrained programming. For the case where the technical coefficients are normally distributed, we present a convergent cutting plane algorithm to solve the equivalent nonlinear program, which takes advantage of the characteristics of the problem. The algorithm requires a moderate computational effort and compares favorably with a general nonlinear code and other approaches proposed for solving this problem.

Stochastic linear knapsack programming problem and its application to a portfolio selection problem

In this paper a probability maximization model of a stochastic linear knapsack problem is considered where the random variables consist of several groups with mutually correlated ones. We propose a solution algorithm to the equivalent nonlinear fractional programming problem with a simple ranking method. This approach will be effectively applied to one of the portfolio selection problems.

Maximation of the signal-to-interference ratio for a doubly spread target: Problems in nonlinear programming

Three optimization problems concerning the maximization of the signal-to-interference ratio for a doubly spread target via signal design are expressed in terms of equivalent nonlinear programming problems defined on a real space by restricting the transmit and processing waveforms to be complex weighted, uniformly spaced pulse trains. Each subpulse can be different in shape and occupy the entire interpulse spacing interval. The approach taken is analogous to the Rayleigh-Ritz technique. The first two optimization problems involve maximization with respect to the complex weights, The third problem involves maximization with respect to the subpulse parameters (e.g., frequency deviation, swept bandwidth, etc.) and allows one to find optimum frequency hop codes. One need not develop algorithms to solve these problems, but rather, one can simply use standard computer programs or methods which are available for solving nonlinear programming problems.

Constrained nonzero-sum games with partially controllable strategies

The present paper deals with a class of nonzero-sum, two-person games with finite strategies when there are constraints on the strategies selected by the players. The constraints arise due to the subjective difficulty that each player often has in assigning to the states probabilities with which he is completely satisfied, and the model specifies how much each player must perturb his initial probability estimate in order to change his maximum utility alternative from the alternative originally best under the initial estimate. It is shown that the Nash-equilibrium solution of this class of nonzero-sum games can be characterized by an equivalent nonlinear program which leads in some cases to a pair of complementary eigenvalue problems. Applications to normal or approximate solutions of linear programming problems are also indicated.