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Bilevel Optimization Problems of Distribution of Interbudgetary Transfers Under Given Limitations
The problems of optimal distribution of transfers within given budget limitations are formulated and analyzed. The mathematical model is presented as...
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Standard Bundle Methods: Untrusted Models and Duality
We review the basic ideas underlying the vast family of algorithms for nonsmooth convex optimization known as “bundle methods”. In a nutshell, these...
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A Proof via Finite Elements for Schiffer’s Conjecture on a Regular Pentagon
A modified version of Schiffer’s conjecture on a regular pentagon states that Neumann eigenfunctions of the Laplacian do not change sign on the...
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MIDAS: A mixed integer dynamic approximation scheme
Mixed integer dynamic approximation scheme (MIDAS) is a new sampling-based algorithm for solving finite-horizon stochastic dynamic programs with...
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On Some Approaches to Find Nash Equilibrium in Concave Games
This paper considers finite-dimensional concave games, i.e., noncooperative n -player games in which the objective functionals are concave in their...
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Some Types of Hypergraphs for Single-Valued Neutrosophic Structures
In this chapter, we present concepts including single-valued neutrosophic hypergraphs, dual single-valued neutrosophic hypergraphs, and transversal...
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A View of Lagrangian Relaxation and Its Applications
We provide an introduction to Lagrangian relaxation, a methodology which consists in moving into the objective function, by means of appropriate...
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Fuzzy Numbers and Fuzzy Optimization
A fuzzy numberFuzzy number is a quantity whose value is imprecise rather than exact as is the case with single-valued number.
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Stochastic hydro-thermal unit commitment via multi-level scenario trees and bundle regularization
For an electric power mix subject to uncertainty, the stochastic unit-commitment problem finds short-term optimal generation schedules that satisfy...
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An approximate solver for multi-medium Riemann problem with Mie–Grüneisen equations of state
We propose an approximate solver for multi-medium Riemann problems with materials described by a family of general Mie–Grüneisen equations of state,...
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Inexact stabilized Benders’ decomposition approaches with application to chance-constrained problems with finite support
We explore modifications of the standard cutting-plane approach for minimizing a convex nondifferentiable function, given by an oracle, over a...
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Logic Puzzles
Puzzles are here illustrated by logic puzzles. They come in various flavours: simple "deduce the rest" from a partial list of facts, knowledge-based...
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Using Machine Learning to Improve Cylindrical Algebraic Decomposition
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier...
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The Mean Value Theorem
This chapter is dedicated entirely to the Mean Value Theorem and its complex history. The opening section offers modern statements of the Mean Value...
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Different Approaches to Multi-Criteria Group Decision Making Problems for Picture Fuzzy Environment
The main objective of proposed work is to introduce a series of picture fuzzy weighted geometric aggregation operators by using t-norm and t-conorm....
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Some Basic Mathematical Exercises
This chapter begins with drill exercises—those used to drill students until they acquire the necessary skills to move on. Drill exercises can range...
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Definitions and Basic Notions
As stated in the introduction, roughly speaking, a radix-β floating-point number x is a number of the form...
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Finding near-optimal independent sets at scale
The maximum independent set problem is NP-hard and particularly difficult to solve in sparse graphs, which typically take exponential time to solve...
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Strong reciprocity and strong consistency in pairwise comparison matrix with fuzzy elements
The decision making problem considered in this paper is to rank n alternatives from the best to the worst, using the information given by the...
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A parallelizable augmented Lagrangian method applied to large-scale non-convex-constrained optimization problems
We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex,...
