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...

In the field of nonlinear programming (in continuous variables) convex analysis [22, 23] plays a pivotal role both in theory and in practice. An analogous theory for discrete optimization (nonlinear integer programming), called " discrete convex analysis " [18, 17], is developed for L-convex and M-convex functions by adapting the ideas in convex analysis and generalizing the results in matroid ...

This paper shows the equivalence between Murota’s L-convex functions and Favati and Tardella’s submodular integrally convex functions: For a submodular integrally convex function g(p1, . . . , pn), the function g̃ defined by g̃(p0, p1, . . . , pn) = g(p1 − p0, . . . , pn − p0) is an L-convex function, and vice versa. This fact implies, in combination with known results for L-convex functions, tha...

Let ∆m = {(t0, . . . , tm) ∈ R : ti ≥ 0, ∑m i=0 ti = 1} be the standard m-dimensional simplex. Let ∅ 6= S ⊂ ⋃ ∞ m=1 ∆m, then a function h : C → R with domain a convex set in a real vector space is S-almost convex iff for all (t0, . . . , tm) ∈ S and x0, . . . , xm ∈ C the inequality h(t0x0 + · · ·+ tmxm) ≤ 1 + t0h(x0) + · · ·+ tmh(xm) holds. A detailed study of the properties of S-almost convex...

Let ∆m = {(t0, . . . , tm) ∈ Rm+1 : ti ≥ 0, ∑m i=0 ti = 1} be the standard m-dimensional simplex and let ∅ = S ⊂ ⋃∞ m=1 ∆m. Then a function h : C → R with domain a convex set in a real vector space is S-almost convex iff for all (t0, . . . , tm) ∈ S and x0, . . . , xm ∈ C the inequality h(t0x0 + · · ·+ tmxm) ≤ 1 + t0h(x0) + · · ·+ tmh(xm) holds. A detailed study of the properties of S-almost co...

In this paper we provide some new necessary and sufficient conditions for pseudoconvexity and semistrict quasiconvexity of a given proper extended real-valued function in terms of the Clarke-Rockafellar subdifferential. Further we extend to programs with pseudoconvex objective function two earlier characterizations of the solutions set of a set constrained nonlinear programming problem due to O...

This is a survey of algorithmic results in the theory of “discrete convex analysis” for integer-valued functions defined on integer lattice points. The theory parallels the ordinary convex analysis, covering discrete analogues of the fundamental concepts such as conjugacy, the Fenchel min-max duality, and separation theorems. The technical development is based on matroid-theoretic concepts, in ...

E-convex function was introduced by Youness 1 and revised by Yang 2 . Chen 3 introduced Semi-E-convex function and studied some of its properties. Syau and Lee 4 defined E-quasi-convex function, strictly E-quasi-convex function and studied some basic properties. Fulga and Preda 5 introduced the class of E-preinvex and E-prequasi-invex functions. All the above E-convex and generalized E-convex f...