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<P>This note formulates a convex mathematical programming problem in which the usual definition of the feasible region is replaced by a significantly different strategy. Instead of specifying the feasible region by a set of convex inequalities, fix â¦ bi, i = 1, 2, ', m, the feasible region is defined via set containment. Here n convex activity sets {Kj, j = 1, 2, ', n} and a convex resource set K are specified and the feasible region is given by <disp-formula><tex-math notation=\"LaTeX\"\\documentclass{aastex} \\usepackage{amsbsy} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{bm} \\usepackage{mathrsfs} \\usepackage{pifont} \\usepackage{stmaryrd} \\usepackage{textcomp} \\usepackage{portland,xspace} \\usepackage{amsmath,amsxtra} \\pagestyle{empty} \\DeclareMathSizes{10}{9}{7}{6} \\begin{document} $$X =\\{x \\in R^{n}\\mid x_{1}K_{1} + x_{2}K_{2} + \\cdots + x_{n}K_{n} \\subseteq K, x_{j}\\geq 0\\}$$ \\end{document}</tex-math></disp-formula> where the binary operation + refers to addition of sets. The problem is then to find xÌ ∈ X that maximizes the linear function c ï¾· x. When the resource set has a special form, this problem is solved via an auxiliary linear-programming problem and application to inexact linear programming is possible.</P>

Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming