In this paper, we present several conditions for the existence of a Lagrange multiplier or a weak saddle point in multiobjective optimization. Relations between a Lagrange multiplier and a weak saddle point are establ...
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In this paper, we present several conditions for the existence of a Lagrange multiplier or a weak saddle point in multiobjective optimization. Relations between a Lagrange multiplier and a weak saddle point are established. A sufficient condition is also given for the equivalence of the Benson proper efficiency and the Borwein proper efficiency.
Owing to the wind and photovoltaic (PV) potential in Brazil, the country has recently seen increased exploration into the construction of wind-PV hybrid plants. However, as specific criteria for contracting this type ...
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Owing to the wind and photovoltaic (PV) potential in Brazil, the country has recently seen increased exploration into the construction of wind-PV hybrid plants. However, as specific criteria for contracting this type of project have not yet been developed, this paper presents a model to assist the government in contracting projects that maximize the socioeconomic well-being of the Brazilian electricity sector. For this, multiobjective programming is used to simultaneously handle two objective functions-maximally reducing emission density and minimizing the levelized cost of electricity (LCOE)-with the aid of the mixture arrangement technique. In this respect, the optimization method called normal boundary intersection (NBI) is applied to solve the multiobjective problem and construct the Pareto frontier. Additionally, a metric based on the ratio between entropy and the global percentage error (GPE) is used to identify the optimal Pareto solution. The model was applied to determine optimal configurations for wind-PV powerplants in twelve Brazilian cities, and the results obtained reveal the capacity of the model to indicate the optimum configuration according to the wind and PV potential of each city.
In the multiobjective programming literature, the concavity of the objectives is usually assumed to be a sufficient condition in seeking Pareto-optimal solutions. This paper investigates nondominated solutions associa...
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In the multiobjective programming literature, the concavity of the objectives is usually assumed to be a sufficient condition in seeking Pareto-optimal solutions. This paper investigates nondominated solutions associated with dominance cones via the assumption of the quasiconcavity of the objectives. Necessary as well as sufficient conditions for such quasiconcave multiobjective programming problems are obtained.
In this paper, Lagrange multiplier theorems are developed for the cases of single-objective and multiobjective programming problems with set functions. Properly efficient solutions are also characterized by subdiffere...
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In this paper, Lagrange multiplier theorems are developed for the cases of single-objective and multiobjective programming problems with set functions. Properly efficient solutions are also characterized by subdifferentials and zero-like functions.
We present a proximal point method to solve multiobjective programming problems based on the scalarization for maps. We build a family of convex scalar strict representations of a convex map F from R(n) to R(m) with r...
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We present a proximal point method to solve multiobjective programming problems based on the scalarization for maps. We build a family of convex scalar strict representations of a convex map F from R(n) to R(m) with respect to the lexicographic order on R(m) and we add a variant of the logarithmic-quadratic regularization of Auslender, where the unconstrained variables in the domain of F are introduced in the quadratic term. The nonegative variables employed in the scalarization are placed in the logarithmic term. We show that the central trajectory of the scalarized problem is bounded and converges to a weak pareto solution of the multiobjective optimization problem.
Using a theorem of Tijs, we derive results about approximate solutions for Nash equilibrium theory and for multiobjective problems. We describe conditions under which one can replace an infinite strategy set, an infin...
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Using a theorem of Tijs, we derive results about approximate solutions for Nash equilibrium theory and for multiobjective problems. We describe conditions under which one can replace an infinite strategy set, an infinite alternative set, or an infinite set of criteria by a finite subset without losing all approximate solutions of the problem under consideration.
A multiobjective programming algorithm may find multiple nondominated solutions. If these solutions are scattered more uniformly over the Pareto frontier in the objective space, they are more different choices and so ...
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A multiobjective programming algorithm may find multiple nondominated solutions. If these solutions are scattered more uniformly over the Pareto frontier in the objective space, they are more different choices and so their quality is better. In this paper, we propose a quality measure called U-measure to measure the uniformity of a given set of nondominated solutions over the Pareto frontier. This frontier is a nonlinear hyper-surface. We measure the uniformity over this hyper-surface in three main steps: 1) determine the domains of the Pareto frontier over which uniformity is measured, 2) determine the nearest neighbors of each solution in the objective space, and 3) compute the discrepancy among the distances between nearest neighbors. The U-measure is equal to this discrepancy where a smaller discrepancy indicates a better uniformity. We can apply the U-measure to complement the other quality measures so that we can evaluate and compare multiobjective programming algorithms from different perspectives.
In this paper, the vector exact l(1) penalty function method for nondifferentiable convex multiobjective programming problems is analyzed. The vector penalized optimization problem with the vector exact l(1) penalty f...
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In this paper, the vector exact l(1) penalty function method for nondifferentiable convex multiobjective programming problems is analyzed. The vector penalized optimization problem with the vector exact l(1) penalty function is defined. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penealized optimization problem with the vector exact l(1) penalty function. This equivalence is established for nondifferentiable vector optimization problems with convex functions. (C) 2012 Elsevier Inc. All rights reserved.
In this paper a vector optimization problem (VOP) is considered where each component of objective and constraint function involves a term containing support function of a compact convex set. Weak and strong Kuhn-Tucke...
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In this paper a vector optimization problem (VOP) is considered where each component of objective and constraint function involves a term containing support function of a compact convex set. Weak and strong Kuhn-Tucker necessary optimality conditions for the problem are obtained under suitable constraint qualifications. Necessary and sufficient conditions are proved for a critical point to be a weak efficient or an efficient solution of the problem (VOP) assuming that the functions belong to different classes of pseudoinvex functions. Two Mond Weir type dual problems are considered for (VOP) and duality results are established.
To facilitate the evaluation of tradeoffs and the articulation of preferences in multiple criteria decision-making, a multiobjective decomposition scheme is proposed that restructures the original problem as a collect...
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To facilitate the evaluation of tradeoffs and the articulation of preferences in multiple criteria decision-making, a multiobjective decomposition scheme is proposed that restructures the original problem as a collection of smaller-sized subproblems with only subsets of the original criteria. A priori preferences on objective tradeoffs are integrated into this process by modifying the ordinary Pareto order by more general domination cones, and decision makers are supported by an interactive decision-making procedure to coordinate any remaining tradeoffs using concepts of approximate efficiency. A theoretical foundation for this method is provided, and an illustrative application to multiobjective portfolio optimization is described in detail. (C) 2009 Elsevier B.V. All rights reserved.
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