Minimizing and Evaluating Weighted Means of Special Mappings

Keywords: Constrained Minimization, Concave Objective-Mappings, Minimum Principle, Optimization/Evaluation Of Weighted Means, Operator-Valued Concave Mappings


A constrained optimization problem is solved, as an application of minimum principle for a sum of strictly concave continuous functions, subject to a linear constraint, firstly for finite sums of elementary such functions. The motivation of solving such problems is minimizing and evaluating the (unknown) mean of a random variable, in terms of the (known) mean of another related random variable. The corresponding result for infinite sums of the such type of functions follows as a consequence, passing to the limit. Note that in our statements and proofs the condition  on the positive numbers  is not essential for the interesting part of the results. So, our work refers not only to means of random variables, but to more general weighted means. A related example is given. A corresponding result for special concave mappings taking values into an order-complete Banach lattice of self-adjoint operators is also proved. Namely, one finds a lower bound for a sum of special concave mappings with ranges in the above mention order-complete Banach lattice, under a suitable linear constraint.


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Author Biographies

Octav Olteanu, Politehnica University of Bucharest

Department of Mathematics-Informatics, Politehnica University of Bucharest, Splaiul Independenței 313, Sector 6, 060042 Bucharest, Romania

Janina Mihaela Mihăilă, Engineering Sciences, Ecological University

Department of Engineering Sciences, Ecological University of Bucharest,Bd. Vasile Milea No. 1G, Sector 6, Bucharest, Romania


M. Yang, X.(J.) Wang, N. Xu, A robust voting machine allocation model to reduce extreme waiting, Omega 57 (2015) 230-237

L. Sun, Li-Zhi Liao, An interior point continuous path-following trajectory for linear programming, Journal of Industrial and Management Optimization, 16, 4 (2019), 1517-1534.

Ya-Z. Dang, J. Sun and Su Zhang, Double projection algorithms for solving the split feasibility problems, Journal of Industrial and Management Optimization, 15, 4 (2019), 2023-2034.

C.P. Niculescu, L.-E. Persson, Convex Functions and Their Applications, Springer-Verlag, 2006.

R.R. Phelps, Lectures on Choquet’s Theorem, D. van Nostrand Company, Inc. Princeton, 1966.

R. B. Holmes, Geometric Functional Analysis and its Applications, Springer, 1975.

R. Cristescu, Functional Analysis, Didactical and Pedagogical Publishing House, Bucharest, 1970 (Romanian).

R. Cristescu, Ordered Vector Spaces and Linear Operators, Academiei, Bucharest, Romania, and Abacus Press, Tunbridge Wells, Kent, England, 1976.

O. Olteanu, J.M. Mihăilă, A class of concave operators and related optimization, U.P.B. Sci. Bulletin Series A, 81, 3 (2019), 165-176.

D. T. Norris, Optimal Solutions to the L_∞ Moment Problem with Lattice Bounds, PhD Thesis. (2002),

University of Colorado, Mathematics Department, 2003.

O. Olteanu, J.M. Mihăilă, Extension and decomposition of linear operators dominated by continuous increasing sublinear operators, U.P.B. Sci. Bull. Series A, 80, 3 (2018), 133-144.

O. Olteanu, Earlier and recent results on convex mappings and convex optimization, MathLAB Journal, Vol. 3 (2019), 136-148.

H. Bonnel, L. Tadjihounde, C. Udrişte, Semivectorial Bilevel Optimization on Riemannian Manifolds, Journal of Optimization Theory and Applications, 167(2) (2015), 464-486.

H. Bonnel, C. Schneider, Post Pareto Analysis and a New Algorithm for the Optimal Parameter Tuning of the Elastic Net, Journal of Optimization Theory and Applications (2019),

M.A. Noor, K.I. Noor and F. Safdar, Generalized geometrically convex functions and inequalities, Journal of

Inequalities and Applications (2017) 2017:202, pp. 1-19.

How to Cite
Olteanu, O., & Mihăilă, J. M. (2019). Minimizing and Evaluating Weighted Means of Special Mappings. MathLAB Journal, 4, 77-86. Retrieved from
Research Articles