In this paper we propose a potential reduction method for smooth convex programming. It is assumed that the objective and constraint functions ful l the socalled Relative Lipschitz Condition, with Lipschitz constant M > 0. The great advantage of this method, above the existing path{following methods, is that it allows linesearches. In our method we do linesearches along the Newton direction wit...

In this paper we propose a large{step analytic center method for smooth convex programming. The method is a natural implementation of the classical method of centers. It is assumed that the objective and constraint functions ful l the socalled Relative Lipschitz Condition, with Lipschitz constant M > 0. A great advantage of the method, above the existing path{following methods, is that the step...

Abstract We present and analyze a new generalized Frank–Wolfe method for the composite optimization problem $$(P): {\min }_{x\in {\mathbb {R}}^n} \; f(\mathsf {A} x) + h(x)$$ ( P ) : min x ∈</mml...

in this paper, an optimization problem with a linear objective function subject to a consistent finite system of fuzzy relation inequalities using the max-product composition is studied. since its feasible domain is non-convex, traditional linear programming methods cannot be applied to solve it. we study this problem and capture some special characteristics of its feasible domain and optimal s...

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

Abstract: We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in R. Our study covers both the case where the true underlying density is log-concave, and where this model is misspecified. We begin by showing that for a sequence of log-concave densities, convergence in distribution implies much s...

Over the past ten years, many examples of natural polynomial families from combinatorics and number theory have emerged whose zeros for high degrees appear to converge to intriguing curves in the complex plane. One interesting collection of examples appears on the website [16] of Richard Stanley which includes chromatic polynomials of complete partite graphs, q-analogue of Catalan numbers, Bern...