mwang@watmath.UUCP (mwang) (05/22/84)
_D_E_P_A_R_T_M_E_N_T _O_F _C_O_M_P_U_T_E_R _S_C_I_E_N_C_E
_U_N_I_V_E_R_S_I_T_Y _O_F _W_A_T_E_R_L_O_O
_S_E_M_I_N_A_R _A_C_T_I_V_I_T_I_E_S
_N_U_M_E_R_I_C_A_L _A_N_A_L_Y_S_I_S _S_E_M_I_N_A_R
- Friday, May 25, 1984.
Prof. R. Fletcher of the University of Dundee will
speak on ``Semi-definite Matrix Constraints in Optimi-
zation.''
TIME: 3:30 PM
ROOM: MC 6091A
ABSTRACT
Positive semi-definite matrix constraints arise in a
number of optimization problems in which some or all of
the elements of a matrix are variables, such as the
educational testing and matrix modification problems.
The structure of such constraints is developed, includ-
ing expressions for the normal cone, feasible direc-
tions and their application to optimality conditions.
A computational framework is given within which these
concepts can be exploited and which permits the quan-
tification of second order effects. The matrix of
Lagrange multipliers in this formulation is shown to
have an important relationship to the characterization
of the normal cone. Modifications of various iterative
schemes in nonlinear programming are considered in ord-
er to develop an effective algorithm for the education-
al testing problem, and comparative numerical experi-
ments are described. It is shown that a particular
choice of the penalty parameter for an l sub 1 exact
penalty function is appropriate for this type of prob-
lem. The behaviour of the extreme eigenvalues (or sums
thereof) of a matrix is related to these ideas.
May 22, 1984