zbMATH — the first resource for mathematics

Duality for d.c. optimization over compact sets. (English) Zbl 1041.90067
Giannessi, Franco (ed.) et al., Optimization theory. Recent developments from Mátraháza. Lectures of the 14th international conference on mathematical programming, Mátraháza, Hungary, March 27–31, 1999. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0009-X). Appl. Optim. 59, 139-146 (2001).
The paper concerns minimization of \(g(x)-h(x)\) subject to a finite number of constraints \(g_i(x)-h_i(x)\leq0\) and \(x\in K\). Here \(K\) is a compact, convex subset of a topological vector space. The value of the problem is stated in terms of some conjugate functions. There are considered two applications: minimization an a not necessarily convex, but compact set; linear programming with \(0\), \(1\) variables.
For the entire collection see [Zbl 0982.00052].

90C46 Optimality conditions and duality in mathematical programming
90C26 Nonconvex programming, global optimization
49N15 Duality theory (optimization)
90C09 Boolean programming
convex duality