Showing papers on "Quadratically constrained quadratic program published in 1990"

An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds

Abstract: This paper gives an O(n) algorithm for a singly constrained convex quadratic program using binary search to solve the Kuhn-Tucker system. Computational results indicate that a randomized version of this algorithm runs in expected linear time and is suitable for practical applications. For the nonconvex case ane-approximate algorithm is proposed which is based on convex and piecewise linear approximations of the objective function.

Quadratic optimization problems in robust beamforming

Abstract: This paper presents a class of constrained optimization problems whereby a quadratic cost function is to be minimized with respect to a weight vector subject to an inequality quadratic constraint on the weight vector. This class of constrained optimization problems arises as a result of a motivation for designing robust antenna array processors in the field of adaptive array processing. The constrained optimization problem is first solved by using the primal-dual method. Numerical techniques are presented to reduce the computational complexity of determining the optimal Lagrange multiplier and hence the optimal weight vector. Subsequently, a set of linear constraints or at most linear plus norm constraints are developed for approximating the performance achievable with the quadratic constraint. The use of linear constraints is very attractive, since they reduce the computational burden required to determine the optimal weight vector.

Bounds for the Quadratic Assignment Problems Using Continuous Optimization Techniques

Abstract: The quadratic assignment problem (denoted QAP), in the trace formulation over the permutation matrices, is min X2 tr(AXB + C)X t : Several recent lower bounds for QAP are discussed. These bounds are obtained by applying continuous optimization techniques to approximations of this combinatorial optimization problem, as well as by exploiting the special matrix structure of the problem. In particular, we apply constrained eigenvalue techniques, reduced gradient methods, subdiierential calculus, generalizations of trust region methods, and sequential quadratic programming.

Stability of linearly constrained convex quadratic programs

Abstract: This paper establishes a simple necessary and sufficient condition for the stability of a linearly constrained convex quadratic program under perturbations of the linear part of the data, including the constraint matrix. It also establishes results on the continuity and differentiability of the optimal objective value of the program as a function of a parameter specifying the magnitude of the perturbation. The results established herein directly generalize well-known results on the stability of linear programs.

An interior-point algorithm for large-scale quadratic problems with box constraints

Abstract: We present computational experience with an interior-point algorithm for large-scale quadratic programming problems with box constraints. The algorithm requires a total of O(√nL) number of iterations, where L is the size of the input data of the problem, and O(n 3) arithmetic operations per iteration. The algorithm has been implemented using vectorization and tested on an IBM 3090-600S computer with vector facilities. The computational results suggest that the efficiency of the algorithm depends on an appropriate choice of parameters. Computational results with various large-scale problems, including examples of obstacle problems, are presented.

A constrained optimization neural net technique for economic power dispatch

Abstract: A linear programming neural network is extended to quadratic programming problems with both linear equality and inequality constraints. It is shown that the equilibrium of the quadratic programming network is asymptotically stable and is in the neighborhood of the minimizer of the objective function. The equilibrium can be made arbitrarily close to the minimizer of the objective function by choosing a parameter sufficiently large. An economic power dispatch problem is simulated to demonstrate the dynamic behavior of the proposed quadratic programming network. >

The Deterministic Equivalents of Chance-Constrained Programming

Abstract: Three concepts combine to show both the feasibility and desirability of incorporating probability within programming models. First, the reliability of estimates obtained by using Chebyshev's inequality increases as variation measured by the coefficient of variation, declines. Second, the coefficient of variation can be substantially reduced by the use of the mean and variance of a truncated normal distribution. Third, chance-constrained programming can be converted into deterministic equivalent quadratic programming by using the parameters of a truncated normal distribution.

Learning control for minimizing a quadratic cost during repetitions of a task

Abstract: In many applications, control systems are asked to perform the same task repeatedly. Learning control laws have been developed over the last few years that allow the controller to improve its performance each repetition, and to converge to zero error in tracking a desired trajectory. This paper generates a new type of learning control law that learns to minimize a quadratic cost function for tracking. Besides being of interest in its own right, this objective alleviates the need to specify a desired trajectory that can actually be performed by the system. The approach used here is to adapt appropriate methods from numerical optimization theory in order to produce learning control algorithms that adjust the system command from repetition to repetition in order to converge to the quadratic cost optimal trajectory.

The singular linear quadratic Gaussian control problem

Abstract: In this paper we discuss the standard LQG control problem for linear, finite-dimensional time-invariant systems without any assumptions on the system parameters. We give an explicit formula for the infimum over all internally stabilizing strictly proper compensators and give a characterization when the infimum is attained.

Comparative Statics and Relative Convexity

Abstract: This paper shows that if the difference of two positive semidefinite matrices is positive semidefinite then the difference of their generalized inverses is negative semidefinite. It uses this to compare comparative static behaviour over feasible sets whose distance functions have Hessians with a positive semidefinite difference. It then interprets this condition in terms of various ideas of the relative convexity of the two sets and relates it to the Le Chatelier principle.

Quadratic programming problems and related linear complementarity problems

Abstract: This paper investigates the general quadratic programming problem, i.e., the problem of finding the minimum of a quadratic function subject to linear constraints. In the case where, over the set of feasible points, the objective function is bounded from below, this problem can be solved by the minimization of a linear function, subject to the solution set of a linear complementarity problem, representing the Kuhn-Tucker conditions of the quadratic problem. To detect in the quadratic problem the unboundedness from below of the objective function, necessary and sufficient conditions are derived. It is shown that, when these conditions are applied, the general quadratic programming problem becomes equivalent to the investigation of an appropriately formulated linear complementarity problem.