Recently, Canovas et al. presented an interesting result: the argmin mapping of a linear semi-infinite program under canonical perturbations is calm if and only if some associated linear semi-infinite inequality syste...
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Recently, Canovas et al. presented an interesting result: the argmin mapping of a linear semi-infinite program under canonical perturbations is calm if and only if some associated linear semi-infinite inequality system is calm. Using classical tools from parametricoptimization, we show that the if-direction of this condition holds in a much more general framework of optimization models, while the opposite direction may fail in the general case. In applications to special classes of problems, we apply a more recent result on the intersection of calm multifunctions.
This paper establishes a new preservation property of supermodularity in a class of two-dimensional parametric optimization problems, where the constraint sets may not be lattices. This property and its extensions uni...
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This paper establishes a new preservation property of supermodularity in a class of two-dimensional parametric optimization problems, where the constraint sets may not be lattices. This property and its extensions unify several results in the literature and provide powerful tools to analyze a variety of operations models including a two-product coordinated pricing and inventory control problem with cross-price effects that we use as an illustrative example.
Recent studies have shown that evolutionary constraint-handling techniques are capable of solving optimizationproblems with constraints. However, these techniques are often evaluated based on benchmark test functions...
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Recent studies have shown that evolutionary constraint-handling techniques are capable of solving optimizationproblems with constraints. However, these techniques are often evaluated based on benchmark test functions instead of real-world problems. This paper presents an application of evolutionary constrained parametricoptimization for a breast cancer immunotherapy model formulated based on biological principles and limited clinical results. It proposes a new constraint-handling technique that partitions the population into different sections to enhance the evolutionary search diversity. In addition, the upper bound of each section is reduced dynamically to drive the convergence of individuals toward the feasible solution region. Experimental results show the effectiveness and robustness of the proposed constraint-handling approach in solving parametric optimization problems. Moreover, the evolutionary optimized cancer immunotherapy model can be used for prognostic outcomes in clinical trials and the predictability is considered significant for such a parametricoptimization approach.
We consider the (linear) parametric 0-1 knapsack problem in which the profits of the items are affine-linear functions of a real-valued parameter and the task is to compute a solution for all values of the parameter. ...
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We consider the (linear) parametric 0-1 knapsack problem in which the profits of the items are affine-linear functions of a real-valued parameter and the task is to compute a solution for all values of the parameter. For this problem, it is known that the piecewise linear convex function mapping the parameter to the optimal objective value of the corresponding instance (called the optimal value function) can have exponentially many breakpoints (points of slope change), which implies that every optimal algorithm for the problem must output a number of solutions that is exponential in the number of items. We provide the first (parametric) polynomial time approximation scheme (PTAS) for the parametric 0-1 knapsack problem. Moreover, we exploit the connection between the parametric problem and the bicriteria problem in order to show that the parametric 0-1 knapsack problem admits a parametric FPTAS when the parameter is restricted to the positive real line and the slopes and intercepts of the affine-linear profit functions of the items are nonnegative. The method used to obtain this result applies to many linear parametric optimization problems and provides a general connection between bicriteria and linear parametric optimization problems. (C) 2016 Elsevier B.V. All rights reserved.
In this paper, we first establish sufficient conditions for the local uniqueness and Holder continuity of perturbed solution set for a scalar optimization problem. Then, by using a linear scalarization method, we obta...
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In this paper, we first establish sufficient conditions for the local uniqueness and Holder continuity of perturbed solution set for a scalar optimization problem. Then, by using a linear scalarization method, we obtain the Holder continuity of two classes of perturbed solution sets for a multiobjective programming problem, respectively. We also give some examples to illustrate that our main results are applicable. These examples are also given to illustrate that our main results are new and different from the ones in literature. (C) 2014 Elsevier Inc. All rights reserved.
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