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A high performance numerical technique in the study of aorto-coronaric bypass anastomoses configurations using steady Stokes equations is presented. The problem is first expressed as an optimal control problem. Then, by using an embedding method, the class of admissible shapes is replaced by a class of positive Borel measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by solving this finite-dimensional linear programming problem. An illustrative example demonstrates the effectiveness of the method.

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Here, a quasi-Newton algorithm for constrained multiobjective optimization is proposed. Under suitable assumptions, global convergence of the algorithm is established.

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‎In this paper, using the idea of convexificators, we study boundedness and nonemptiness of Lagrange multipliers satisfying the first order necessary conditions. We consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. Within this context, define generalized Mangasarian-Fromovitz constraint qualification and show that the constraint qualification are necessary and suficient conditions for the Karush- Kuhn-Tucker(KKT) multipliers set to be nonempty and bounded.

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‎It is a well-known fact that finding a minimum dominating set and consequently the domination number of a general graph is an NP-complete problem‎. ‎In this paper‎, ‎we first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxations‎. ‎For each of these relaxations‎, ‎different rounding algorithm is exploited to produce a near-optimal dominating set‎. ‎Feasibility of the generated solutions and efficiency of the algorithms are analyzed as well‎.

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In this paper, we propose an arc-search corrector-predictor
interior-point method for solving $P_*(kappa)$-linear
complementarity problems. The proposed algorithm searches the
optimizers along an ellipse that is an approximation of the central
path. The algorithm generates a sequence of iterates in the wide
neighborhood of central path introduced by Ai and Zhang. The
algorithm does not depend on the handicap $kappa$ of the problem,
so that it can be used for any $P_*(kappa)$-linear complementarity
problem. Based on the ellipse approximation of the central path and
the wide neighborhood, we show that the proposed algorithm has
$O((1+kappa)sqrt{n}L)$ iteration complexity, the best-known
iteration complexity obtained so far by any interior-point method
for solving $P_*(kappa)$-linear complementarity problems.

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Clustering problems with the similarity measure defined by the $𝐿_1$-norm are studied. Characterizations of different stationary points of these problems are given using their difference of convex representations. An algorithm for finding the Clarke stationary points of the clustering problems is designed and a clustering algorithm is developed based on it. The clustering algorithm finds a center of a data set at the first iteration and gradually adds one cluster center at each consecutive iteration. The proposed algorithm is tested using large real world data sets and compared with other clustering algorithms.

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In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator function. Relation between weak subifferential and augmented normal cone and epigraph is also explored. We also obtain optimality conditions via weak subdifferential and augmented normal cone. Finally, we define the Stampacchia and Minty solution via weak subdifferential and investigate the relation between Stampacchia and Minty solution and the minimal point.

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We consider the extended trust region subproblem (eTRS) as the minimization of an indefinite quadratic function subject to the intersection of unit ball with a single linear inequality constraint. Using a variation of the S-Lemma, we derive the necessary and sufficient optimality conditions for eTRS. Then, an OCP/SDP formulation is introduced for the problem. Finally, several illustrative examples are provided.

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We deal with a recently proposed method of Chubanov [1], for solving linear homogeneous systems with positive variables. We use Nesterov's excessive gap method in the basic procedure. As a result, the iteration bound for the basic procedure is reduced by the factor $nsqrt{n}$. The price for this improvement is that the iterations are more costly, namely $O(n^2 )$ instead of $O(n)$. The overall gain in the complexity hence becomes a factor of $sqrt{n}$.

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The conjugate gradient method (CGM) stands out as one of the most rapidly growing and effective approaches for addressing unconstrained optimization problems. In recent years, significant efforts have been dedicated to adapting the CGM for tackling nonlinear optimization challenges. This research article introduces a new modification of the Fletcher–Reeves (FR) conjugate gradient projection method. The proposed method is characterized by its sufficient descent property, and its global convergence has been established under specific assumptions. Numerical experiments conducted on a range of functions from the CUTEr collection demonstrate the potential and effectiveness of the proposed methods.
 

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In this paper, we investigate a solution procedure for a fuzzy linear fractional optimization problem in which the input parameters are considered as convex fuzzy numbers. By applying a specific fuzzy ranking method which is based on the α-cut concept, and according to Charnes and Cooper’s approach of variable transformation, the solution of the original fuzzy linear fractional optimization model is transformed to the solution of at most two semi-infinite linear programs that are dis similar among themselves via a sign in a constraint and in the objective function. An appropriate cutting plane algorithm(CPA) of Fang is uti lized to obtain the optimal solution of the semi-infinite linear programs. Further, the application of our provided algorithm in facility location theory is discussed properly. Finally, an illustrative example is given to clarify the developed solution procedure.

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Coordination is a critical factor in optimizing supply chain performance. Given the pervasive uncertainties in supply chain management, it is essential to develop decisions that are robust against these uncertainties while preserving operational efficiency. This paper aims to determine an optimal supply chain policy that ensures the total system cost remains robust against correlated uncertainties in demand and lead time. To address the correlation among demand data and avoid overly conservative solutions, a novel robust optimization model is proposed based on a correlated polyhedral uncertainty set. This approach explicitly accounts for demand correlation, thereby reducing the price of robustness. Numerical results demonstrate that integrating coordination as a strategic decision and employing robust optimization as a tactical tool significantly enhances supply chain performance. Moreover, incorporating demand correlation in the proposed model leads to a substantial reduction in the price of robustness and, consequently, higher supply chain profitability. Extending this framework to more complex supply chain models with multiple sources of uncertainty holds great potential for further improving the robustness and practical applicability of supply chain decision-making.
 

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The line location problem, which represents a specific case within the broader class of hyperplane location problems, has attracted considerable research focus location theory. This investigation addresses locating lines from a location science perspective. Given n points situated in the plane, each assigned a positive weight that reflects its relative importance, the median line is defined as the line minimizing the total sum of these weighted distances. Our study is, to our knowledge, the first to examine the inverse median line location problem in the plane under both the Euclidean and rectilinear distance norms. Specifically, when a line L is fixed, the goal is to determine the Minimum-cost modifications to the problem parameters—either the demand point weights or their spatial coordinates—such that L becomes the globally optimal median line. We proceed by developing and analyzing mathematical models that characterize this inverse problem across the two norm settings. We demonstrate that the inverse model, when demand weights are the variables, can be precisely formulated and solved via linear programming. Conversely, for the instance involving necessary modifications to the coordinates, an effective greedy algorithm is proposed for solution approximation. The practical application and performance of this developed methodology are subsequently illustrated through a set of computational experiments.