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Explicit solutions of infinite quadratic programs

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Abstract

LetH be a Hilbert space,X be a real Banach space,A: H→X be an operator withD (A) dense inH, G: H→H be positive definite,xD (A) andbH. Consider the quadratic programming problem:

$$\begin{gathered} QP:Minimize \frac{1}{2}\left\langle {p,x} \right\rangle + \left\langle {x,Gx} \right\rangle \hfill \\ subject to Ax = b \hfill \\ \end{gathered} $$

In this paper, we obtain an explicit solution to teh above problem using generalized inverses.

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Author information

Correspondence to K. C. Sivakumar.

Additional information

Sivakumar K.C. received his Ph.D from Indian Institute of Technology, Chennai. He has been working as a lecturer at Anna University since December 1995. His research interests are in infinite linear programming and operator theory of generalized inverses.

Mercy Swarna J. received her M.Sc degree from Anna University, Chennai, Tamil Nadu in 2000. Since then she has been a research scholar at Anna University. Her research interest is Mathematical Programming.

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Sivakumar, K.C., Swarna, J.M. Explicit solutions of infinite quadratic programs. JAMC 12, 211 (2003). https://doi.org/10.1007/BF02936193

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AMS Mathematics Subject Classification

  • Primary 90C20
  • Secondary 95A09

Key words and phrases

  • Infinite quadratic programs
  • dual pairs of vector spaces
  • generalized inverses