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One of the most difficult fractional programs encountered so far is the sum-of-ratios problem. Contrary to earlier expectations it is much more removed from convex programming than other multi-ratio problems analyzed before. It really should be viewed in the context of global optimization. It proves to be essentially N P-complete in spite of its special(More)
We review some recent developments in single-ratio and generalized fractional programming. In the latter case we focus on the maximization of the smallest of several ratios. To introduce these newer results, we provide the necessary context by including some major existing results [63]. In this concise survey we consider applications, theory and algorithms.
OBJECTIVE Predictions of the binding ability of antigen peptides to major histocompatibility complex (MHC) class II molecules are important in vaccine development. The variable length of each binding peptide complicates this prediction. METHODOLOGY Motivated by the search properties of the ant colony system (ACS), a method for the identification of an(More)
The following problem is considered in this paper : max x∈D { m j=1 g j (x)/h j (x)}, where g j (x) ≥ 0 and h j (x) > 0, j = 1, · · · , m are d.c. (difference of convex) functions over a convex compact set D in R n. Specifically, it is reformulated into the problem of maximizing a linear objective function over a feasible region defined by multiple reverse(More)
Previous studies have shown that the deletion of brnQ from the Corynebacterium glutamicum chromosome results in a significant reduction in l-isoleucine uptake rates, while overexpression of brnFE leads to enhanced l-isoleucine export rates. Given that net excretion rates would be an important factor for high titers of l-isoleucine accumulation, we have(More)
Acetate is a primary inhibitory metabolite in Escherichia coli cultivation which is detrimental to bacterial growth and the formation of desired products. It can be derived from acetyl coenzyme A by the phosphotransacetylase (Pta)–acetate kinase (AckA) pathway. In this study, the fermentation characteristics of Pta mutant strain E. coli TRTHΔpta were(More)
We consider a global minimization problem: min{cT-c+dT 1-c E X, y G Y ^h, (X , Y) â F}, where X and Y are polytopes in Rnl and Rn2, respectively; F is a closed convex set in R"~'"~; and Gh (h = l , ,. . , m 2) is an open convex set in Rn2. We propose an alogorithm based on a combination of polyhedral outer approximation, branch-and-bound and cutting plane(More)