Using a multiple-objective framework, feasible linear complementarity problems (LCPs) are handled in a unified manner. The resulting procedure either solves the feasible LCP or, under certain conditions, produces an a...
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Using a multiple-objective framework, feasible linear complementarity problems (LCPs) are handled in a unified manner. The resulting procedure either solves the feasible LCP or, under certain conditions, produces an approximate solution which is an efficient point of the associated multiple-objective problem. A mathematical existence theory is developed which allows both specialization and extension of earlier results in multiple-objective programming. Two perturbation approaches to finding the closest solvable LCPs to a given unsolvable LCP are proposed. Several illustrative examples are provided and discussed.
Decision environments involve the need to solve problems with varying degrees of uncertainty as well as multiple, potentially conflicting objectives. Chance constraints consider the uncertainty encountered. Codes inco...
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Decision environments involve the need to solve problems with varying degrees of uncertainty as well as multiple, potentially conflicting objectives. Chance constraints consider the uncertainty encountered. Codes incorporating chance constraints into a mathematical programming model are not available on a widespread basis owing to the non-linear form of the chance constraints. Therefore, accurate linear approximations would be useful to analyse this class of problems with efficient linear codes. This paper presents an approximation formula for chance constraints which can be used in either the single- or multiple-objective case. The approximation presented will place a bound on the chance constraint at least as tight as the true non-linear form, thus overachieving the chance constraint at the expense of other constraints or objectives.
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