Journal of the Operations Research Society of China

This paper is concerned with the problem of modifying the edge lengths of a weighted extended star network with n vertices by integer amounts at the minimum total cost subject to be given modification bounds so that a set of p prespecified vertices becomes an undesirable p-median location on the perturbed network. We call this problem as the integer inverse undesirable p-median location model. Exact combinatorial algorithms with $$ {\mathcal {O}}\left( p^2 n \log n\right) $$ and $${{\mathcal {O}}}\left( p^{2}(n \log n+ n \log \eta _{\max })\right) $$ running times are proposed for solving the problem under the weighted rectilinear and weighted Chebyshev norms, respectively. Furthermore, it is shown that the problem under the weighted sum-type Hamming distance with uniform modification bounds can be solved in $$ {\mathcal {O}}(p^2n \log n)$$ time.

We propose a two-phase-SQP (Sequential Quadratic Programming) algorithm for equality-constrained optimization problem. In this paper, an iteration process is developed, and at each iteration, two quadratic sub-problems are solved. It is proved that, under some suitable assumptions and without computing further higher-order derivatives, this iteration process achieves higher-order local convergence property in comparison to Newton-SQP scheme. Theoretical advantage and a note on $$l_{1}$$ merit function associated to the method are provided.

This work explores a family of two-block nonconvex optimization problems subject to linear constraints. We first introduce a simple but universal Bregman-style improved alternating direction method of multipliers (ADMM) based on the iteration framework of ADMM and the Bregman distance. Then, we utilize the smooth performance of one of the components to develop a linearized version of it. Compared to the traditional ADMM, both proposed methods integrate a convex combination strategy into the multiplier update step. For each proposed method, we demonstrate the convergence of the entire iteration sequence to a unique critical point of the augmented Lagrangian function utilizing the powerful Kurdyka–Łojasiewicz property, and we also derive convergence rates for both the sequence of merit function values and the iteration sequence. Finally, some numerical results show that the proposed methods are effective and encouraging for the Lasso model.

In this paper, we consider approximation algorithms for optimizing a generic multivariate polynomial function in discrete (typically binary) variables. Such models have natural applications in graph theory, neural networks, error-correcting codes, among many others. In particular, we focus on three types of optimization models: (1) maximizing a homogeneous polynomial function in binary variables; (2) maximizing a homogeneous polynomial function in binary variables, mixed with variables under spherical constraints; (3) maximizing an inhomogeneous polynomial function in binary variables. We propose polynomial-time randomized approximation algorithms for such polynomial optimization models, and establish the approximation ratios (or relative approximation ratios whenever appropriate) for the proposed algorithms. Some examples of applications for these models and algorithms are discussed as well.

In this work, we explore a nonsmooth semi-infinite multiobjective fractional interval-valued optimization problem. Using an adequate constraint qualification, we establish necessary optimality conditions in terms of Karush–Kuhn–Tucker multipliers and upper semiregular convexificators. We do not assume that the interval-valued objective function is smooth or that it is convex. There are examples highlighting both our results and the limits of certain past studies.

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