Constructing optimal designs with constraints

• Published in: Journal of statistical planning and inference Vol. 128; no. 2; pp. 609 - 621
• Main Authors: Mandal, S., Torsney, B., Carriere, K.C.
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.02.2005; New York,NY Elsevier Science; Amsterdam
• Subjects: Constrained optimality; Constraints; Directional derivatives; Exact sciences and technology; Experimental design; Lagrangian approach; Mathematics; Multiplicative algorithms; Optimality conditions; Probability and statistics; Sciences and techniques of general use; Statistics; Sufficiency and information; Optimality conditions; Constraints; primary 62K05; secondary 62B15; Directional derivatives; Lagrangian approach; Multiplicative algorithms; Constrained optimality; Statistical method; Multiplicative algorithm; Experimental design; Weight function; Convergence rate; Optimality condition; Statistical decision; Optimal design(statistics); Lagrangian method; Constrained optimization
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2003.12.003

We construct constrained approximate optimal designs by maximizing a criterion subject to constraints. We approach this problem by transforming the constrained optimization problem to one of maximizing three functions of the design weights simultaneously. We used a class of multiplicative algorithms, indexed by a function f(·). These algorithms are shown to satisfy the basic constraints on the design weights of nonnegativity and summation to unity. We also investigate techniques for improving convergence rates by means of some suitable choices of the function f(·).