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[For the entire collection see Zbl 0571.00016.] Improper problems of convex quadratic programming in the form (1) $\max \{-α(x-p)\sp TQ(x-p)+(c,x):$ Ax$\le b\}$, $α>0$ are analyzed by taking them as a result of regularizing the linear programming problem (2) max$\{$ (c,x): Ax$\le b\}$. The system Ax$\le b$ in (1) is decomposed into subsystems $A\sb jx\le b\sp j$ $(j=0,1,...,m\sb 0)$, with consistent subsystem $A\sb 0x\le b\sp 0$. Theorems about the dual problems are formulated containing new useful information on the regularization of linear programming problems which are not necessarily solvable. For the case of $Q=E$ the resulting primal problem can be obtained by applying the penalty function method and the regularization of linear problems due to {\it A. N. Tikhonov} and {\it V. Ya. Arsenin} ["Solution methods for ill-posed problems" (1974; Zbl 0309.65002)]. This problem is also shown to have an approximative sense.