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Necessary optimality conditions for a bilevel optimization problem are given in the paper by Kohli (J Optim Theory Appl 152: 632–651, 2012). Recently, the same author corrected his results in the note (J Optim Theory Appl 181:706–707, 2019). In this work, we have pointed out that some of the new modifications are wrong. We correct the flaws and present an alternative proof for the main result. [ABSTRACT FROM AUTHOR]

The numerical algorithm by Cristofari et al. modifies the augmented Lagrangian method ALGENCAN proposed by Andreani and his collaborators by incorporating certain second-order information into the augmented Lagrangian framework. Professor Franco Giannessi, University of Pisa, is an outstanding mathematician whose contributions to optimization theory and its applications and to the world optimization community are difficult to overstate. The paper by Izmailov and Solodov introduces and develops a novel perturbed augmented Lagrangian method framework for constrained optimization problems. [Extracted from the article]

We propose a spatial equilibrium problem for a pulp and paper supply chain network under the Emission Trading System (ETS) and the circular economy principles. The developed closed-loop supply chain model, based on the variational inequality theory, accounts for the forest deployment and the production of paper using both virgin pulp and recyclable paper waste in an area that is subject to the ETS. In addition, it considers the exchanges of virgin pulp, paper, recyclable and not-recyclable paper waste between this regulated area and geographical zones where no environmental policies apply. The aim of this paper is to investigate the ETS impacts on the pulp and paper industries located in an environmentally regulated area in terms of operating costs, production and trading volumes of the aforementioned commodities, and emissions generated. The case study focuses on the European pulp and paper companies, which are among the energy-intensive industries deemed to be exposed to the carbon leakage risk as a consequence of the ETS application. Sensitivity analyses on the carbon price value and on the trade flexibility are conducted. Our results show that the ETS implies additional costs for the European pulp and paper companies and induces them to resort more on imports of virgin pulp and paper from not-regulated zones. [ABSTRACT FROM AUTHOR]

In this work, some counterexamples are given to refute some results in the paper by Guo and Li (J Optim Theory Appl 162:821–844, 2014). We correct the faulty in some of their theorems, and we present alternative proofs. Moreover, we extend the definition of approximately pseudo-dissipative in the setting of metrizable topological vector spaces. [ABSTRACT FROM AUTHOR]

This Forum Note concerns the question of necessary optimality conditions in optimal control problems subject to state constraints. Some critical remarks about a recently published paper are made. [ABSTRACT FROM AUTHOR]

In this short paper, we look into a conclusion drawn by Alzalg (J Optim Theory Appl 169:32-49, 2016). We think the conclusion drawn in the paper is incorrect by pointing out three things. First, we provide a counterexample that the proposed inner product does not satisfy bilinearity. Secondly, we offer an argument why a pth-order cone cannot be self-dual under any reasonable inner product structure on $$\mathbb {R}^n$$ . Thirdly, even under the assumption that all elements operator commute, the inner product becomes an official inner product and the arbitrary-order cone can be shown as a symmetric cone, we think this condition is still unreasonable and very stringent so that the result can only be applied to very few cases. [ABSTRACT FROM AUTHOR]

In this note, we give affirmative answers to two open problems posed by Agarwal et al. in the paper (J Optim Theory Appl 163(2):482-490, ). [ABSTRACT FROM AUTHOR]

This note tries to answer issues raised in Bhardwaj and Kumar (J Optim Theory Appl 163(2): 685-696, 2014). The research summarizes that the results obtained in Khan et al. (J Optim Theory Appl 159: 536-546, 2013) are sound and correct and it fulfills all the necessary requirements of its scope and objectives. [ABSTRACT FROM AUTHOR]

In this note, we correct a mistake in the paper (López et al., J Optim Theory Appl 159(3):741-768, ). [ABSTRACT FROM AUTHOR]

With this note, we want to open a discussion on the duality theory for Interval Optimization. We begin by showing that some duality results Wu ( J Optim Theory Appl 144:615-628, ) are useless. [ABSTRACT FROM AUTHOR]