On the minimum-norm solution of convex quadratic programming

Constrained Minimization Problem

We discuss some basic concepts and present a numerical procedure for finding the minimum-norm solution of convex quadratic programs (QPs) subject to linear equality and inequality constraints. Our approach is based on a theorem of alternatives and on a convenient characterization of the solution set of convex QPs. We show that this problem can be reduced to a simple constrained minimization problem with a once-differentiable convex objective function. We use finite termination of an appropriate Newton's method to solve this problem. Numerical results show that the proposed method is efficient.

An extended alternating direction method for variational inequality problems with linear equality and inequality constraints

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.05.205 ◽

2007 ◽

Vol 184 (2) ◽

pp. 769-782 ◽

Cited By ~ 4

Author(s):

Zhong Zhou ◽

Anthony Chen ◽

Deren Han

Keyword(s):

Variational Inequality ◽

Inequality Constraints ◽

Alternating Direction Method ◽

Variational Inequality Problems ◽

Linear Equality ◽

Alternating Direction ◽

A Note on Applying the BCH Method Under Linear Equality and Inequality Constraints

Journal of Classification ◽

10.1007/s00357-018-9298-2 ◽

2018 ◽

Vol 36 (3) ◽

pp. 566-575

Author(s):

L. Boeschoten ◽

M. A. Croon ◽

D. L. Oberski

Keyword(s):

Inequality Constraints ◽

Linear Equality ◽

A new affine scaling interior point algorithm for nonlinear optimization subject to linear equality and inequality constraints

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(03)00458-8 ◽

2003 ◽

Vol 161 (1) ◽

pp. 1-25 ◽

Cited By ~ 11

Author(s):

Detong Zhu

Keyword(s):

Nonlinear Optimization ◽

Interior Point ◽

Inequality Constraints ◽

Affine Scaling ◽

Interior Point Algorithm ◽

Linear Equality ◽

Constrained Discrimination via MDI Estimation: The use of Additional Information in Segmentation Analysis

Journal of Marketing Research ◽

10.1177/002224378702400407 ◽

1987 ◽

Vol 24 (4) ◽

pp. 396-403 ◽

Cited By ~ 1

Author(s):

Ajith Kumar ◽

William R. Dillon

Keyword(s):

Inequality Constraints ◽

Target Population ◽

Additional Information ◽

Linear Equality ◽

Segmentation Analysis ◽

Discrimination Information ◽

Multinomial Probabilities ◽

Minimum Discrimination Information ◽

Discrimination Method

The authors demonstrate a general, flexible constrained discrimination method for testing hypotheses about the segmentability of a target population using categorical descriptors when additional information is available. The method applies the principle of minimum discrimination information (MDI) to the estimation of multinomial probabilities under linear equality and inequality constraints.

A dual neural network for convex quadratic programming subject to linear equality and inequality constraints

Physics Letters A ◽

10.1016/s0375-9601(02)00424-3 ◽

2002 ◽

Vol 298 (4) ◽

pp. 271-278 ◽

Cited By ~ 112

Author(s):

Yunong Zhang ◽

Jun Wang

Keyword(s):

Neural Network ◽

Quadratic Programming ◽

Inequality Constraints ◽

Convex Quadratic Programming ◽

Linear Equality ◽

Polyhedral Combinatorics and Neural Networks

Neural Computation ◽

10.1162/neco.1994.6.1.161 ◽

1994 ◽

Vol 6 (1) ◽

pp. 161-180 ◽

Cited By ~ 52

Author(s):

Andrew H. Gee ◽

Richard W. Prager

Keyword(s):

Neural Networks ◽

Ad Hoc ◽

Inequality Constraints ◽

Polyhedral Combinatorics ◽

Knapsack Problems ◽

Linear Equality ◽

Learning Technique ◽

Valid Solution ◽

Modified Dynamics

The often disappointing performance of optimizing neural networks can be partly attributed to the rather ad hoc manner in which problems are mapped onto them for solution. In this paper a rigorous mapping is described for quadratic 0-1 programming problems with linear equality and inequality constraints, this being the most general class of problem such networks can solve. The problem's constraints define a polyhedron P containing all the valid solution points, and the mapping guarantees strict confinement of the network's state vector to P. However, forcing convergence to a 0-1 point within P is shown to be generally intractable, rendering the Hopfield and similar models inapplicable to the vast majority of problems. A modification of the tabu learning technique is presented as a more coherent approach to general problem solving with neural networks. When tested on a collection of knapsack problems, the modified dynamics produced some very encouraging results.

Inference with Linear Equality and Inequality Constraints UsingR: The Packageic.infer

Journal of Statistical Software ◽

10.18637/jss.v033.i10 ◽

2010 ◽

Vol 33 (10) ◽

Cited By ~ 11

Author(s):

Ulrike Grömping

Keyword(s):

Inequality Constraints ◽

Linear Equality ◽

Stability of 1-Bit Compressed Sensing in Sparse Data Reconstruction

Mathematical Problems in Engineering ◽

10.1155/2020/8849395 ◽

2020 ◽

Vol 2020 ◽

pp. 1-14

Author(s):

Yuefang Lian ◽

Jinchuan Zhou ◽

Jingyong Tang ◽

Zhongfeng Sun

Keyword(s):

Optimization Problems ◽

Inequality Constraints ◽

Necessary Condition ◽

Sensing Matrix ◽

Quadratic Constraint ◽

Linear Equality ◽

Sufficient And Necessary Condition

Measurement Vector ◽

The Stability ◽

1-bit compressing sensing (CS) is an important class of sparse optimization problems. This paper focuses on the stability theory for 1-bit CS with quadratic constraint. The model is rebuilt by reformulating sign measurements by linear equality and inequality constraints, and the quadratic constraint with noise is approximated by polytopes to any level of accuracy. A new concept called restricted weak RSP of a transposed sensing matrix with respect to the measurement vector is introduced. Our results show that this concept is a sufficient and necessary condition for the stability of 1-bit CS without noise and is a sufficient condition if the noise is available.