نتایج جستجو برای: m convex function

تعداد نتایج: 1717049  

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

Journal: :SIAM Journal on Optimization 2012
Bingsheng He Min Tao Xiaoming Yuan

We consider the linearly constrained separable convex programming whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method (ADM) has been well studied in the literature for the special case m = 2. But the convergence of extending ADM to the general case m ≥ 3 is still open. In this paper, we show that the straightf...

1995
Franck Nielsen Mariette Yvinec

A set of planar objects is said to be of type m if the convex hull of any two objects has its size bounded by 2m. In this paper, we present an algorithm based on the marriage-before-conquest paradigm to compute the convex hull of a set of n planar convex objects of xed type m. The algorithm is output-sensitive, i.e. its time complexity depends on the size h of the computed convex hull. The main...

2002
Kazuo MUROTA Akiyoshi SHIOURA

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions defined over the real space. In this paper, we consider a ...

2007
Satoko MORIGUCHI Nobuyuki TSUCHIMURA

We consider the problem of minimizing a nonlinear discrete function with L-/M-convexity proposed in the theory of discrete convex analysis. For this problem, steepest descent algorithms and steepest descent scaling algorithms are known. In this paper, we use continuous relaxation approach which minimizes the continuous variable version first in order to find a good initial solution of a steepes...

2007
R. H. BING

A subset M of a topological space 5 is said to have a convex metric (even though S may have no metric) if the subspace M of 5 has a convex metric. It is known [5 J that a compact continuum is locally connected if it has a convex metric. The question has been raised [5] as to whether or not a compact locally connected continuum M can be assigned a convex metric. Menger showed [5] that M is conve...

Journal: :J. Global Optimization 2002
Olvi L. Mangasarian

Characterization of the containment of a polyhedral set in a closed halfspace, a key factor in generating knowledge-based support vector machine classifiers [7], is extended to the following: (i) Containment of one polyhedral set in another. (ii) Containment of a polyhedral set in a reverse-convex set defined by convex quadratic constraints. (iii) Containment of a general closed convex set, def...

2004
Kazuo MUROTA

The infimal convolution of M-convex functions is M-convex. This is a fundamental fact in discrete convex analysis that is often useful in its application to mathematical economics and game theory. M-convexity and its variant called M-convexity are closely related to gross substitutability, and the infimal convolution operation corresponds to an aggregation. This note provides a succinct descrip...

Journal: :Filomat 2021

In this paper, we point out that the proof of Theorem 2.4(5), Proposition 2.6(1) and 2.8(1) in paper titled ?On (L,M)-fuzzy convex structures? (Filomat 33(13): 4151-4163, 2019) are not true general. Then, give three correct proofs these results

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