Optimization Letters最新文献

We study a single machine scheduling problem with generalized due-dates and general position-dependent job processing times. The objective function is minimum number of tardy jobs. The problem is proved to be NP-hard in the strong sense. We introduce an efficient algorithm that solves medium size problems in reasonable running time. A simple and efficient heuristic is also introduced, which obtained the optimal solution in the vast majority of our tests.

In this paper, we consider the numerical solution of a class of vertical tensor complementarity problems. By reformulating the involved vertical tensor complementarity problem (VTCP) as an equivalent projected fixed point equation, together with the relevant properties of the power Lipschitz tensor, we propose a projected fixed point method for the involved VTCP, and discuss its convergence properties. Numerical experiments are given to illustrate the effectiveness of the proposed method.

We are given a set of indivisible goods and a set of m agents where each good has a size and each agent has an additive valuation function and a budget. The budgeted maximin share allocation problem is to find a feasible allocation such that the size of the bundle allocated to each agent does not exceed its budget, and the minimum ratio of the valuation and the maximin share (MMS) value of any agent is as large as possible, where the MMS value of each agent is that he can achieve by dividing the goods into n bundles, and receiving his least desirable bundle. In this paper, we prove the existence of (frac{n}{3n-2})-approximate MMS allocation and give an instance which does not have a ((frac{3}{4}+epsilon ))-approximate MMS allocation, for any (epsilon in (0,1)). Moreover, we provide a polynomial time algorithm to find an (frac{1}{3})-MMS allocation, and prove that there is no ((frac{2}{3} + epsilon ))-approximate algorithm in polynomial time unless (mathcal{P}=mathcal{N}mathcal{P}).

We introduce and study some explicit iterative algorithms for solving the system of split equality problems in Hilbert spaces. The strong convergence of the proposed algorithms is proved by using some milder conditions put on control parameters than the one used in Tuyen (Bull Malays Math Sci Soc 46:44, 2023).

We establish the optimal ergodic convergence rate for the classical projected subgradient method with time-varying step-sizes. This convergence rate remains the same even if we slightly increase the weight of the most recent points, thereby relaxing the ergodic sense.

This work deals with a Berge equilibrium problem (BEP). Based on the existence results of Berge equilibrium of Nessah et al. (Appl Math Lett 20(8):926–932. 2007), we consider BEP with concave objective functions. The existence of Berge equilibrium has been proven. BEP reduces to nonsmooth optimization problem. Then using a regularized function, we reduce a problem of finding Berge equilibrium to a nonconvex global optimization problem with a differentiable objective functions. The later allows to apply optimization methods and algorithms to solve the original problem.

The weighted linear complementarity problem (wLCP) can be used for modelling a large class of problems from science and economics. In this paper, we introduce a new class of weighted complementarity functions and show that it is continuously differentiable everywhere. By using this function, we propose a two steps Levenberg–Marquardt-type method to solve the wLCP. Under suitable conditions, we prove that the proposed method is globally convergent and the generated iteration sequence is bounded. Moreover, we show that the proposed method has cubic convergence rate under the local error bound condition. Some numerical results are reported.

In this paper, we present a Levenberg–Marquardt algorithm for nonlinear equations, where the exact Jacobians are unavailable, but their model approximations can be built in some random fashion. We study the complexity of the algorithm and show that the upper bound of the iteration numbers in expectation to obtain a first order stationary point is (O(epsilon ^{-3})).

One of the most significant challenges in logistics today is managing the complexity, uncertainty, and dynamism of the market. External and internal factors highly influence the efficiency of operations processes. Cross-docking Distribution Centers are one way of adopting a real-time philosophy. This work provides a Stability Approach (SA) for solving multi-dock truck scheduling problems under truck release date uncertainty. We consider time-based objectives for optimization and propose two new heuristics to obtain viable solutions for them. To evaluate the performance of the SA, we develop and analyze two other different scheduling policies, namely, Without Adjustments and Perfect Information. Extensive computational experiments allow us to compare SA with others and show that the methodology can support managers in their daily cross-docking operations, efficiently handling dynamic and uncertain data, and making good decisions quickly.