In this paper some simple ideas about ordered sets and inverse functions are developed into a theory of inverse pairs of optimization problems. This relationship is shown to permit the use of root-finding methods to f...
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The paper is a manifestation of the fundamental importance of the linear program with linear complementarity constraints (LPCC) in disjunctive and hierarchical programming as well as in some novel paradigms of mathema...
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The paper is a manifestation of the fundamental importance of the linear program with linear complementarity constraints (LPCC) in disjunctive and hierarchical programming as well as in some novel paradigms of mathematical programming. In addition to providing a unified framework for bilevel and inverse linear optimization, nonconvex piecewise linear programming, indefinite quadratic programs, quantile minimization, and a"" (0) minimization, the LPCC provides a gateway to a mathematical program with equilibrium constraints, which itself is an important class of constrained optimization problems that has broad applications. We describe several approaches for the global resolution of the LPCC, including a logical Benders approach that can be applied to problems that may be infeasible or unbounded.
inverse optimization is one of the interesting areas in both fundamental and applied research. This paper introduces a new approach, named as Khalifa, Kumar, and Mirjalili (KKM) approach, for solving the inverse capac...
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inverse optimization is one of the interesting areas in both fundamental and applied research. This paper introduces a new approach, named as Khalifa, Kumar, and Mirjalili (KKM) approach, for solving the inverse capacitated transportation problem (ICTP) in a neutrosophic environment. The problem is considered with unit transportation cost associated with the single-valued trapezoidal neutrosophic numbers. Using the proposed KKM approach, the objective of the research work is to make the transportation cost as low as possible, which can lead to an optimal feasible solution. Based on the score function, the neutrosophic problem is first converted into an equivalent deterministic problem and then into a linear programming (LP) problem. Afterwards, by applying the dual and optimality conditions the inverse problem is obtained. In the end, an illustrative example is given to support the proposed approach and to gain more insights.
We survey fundamental concepts for inverse programming and then present the Universal Resolving Algorithm, an algorithm for inverse computation in a first order, functional programming language. We discuss the key co...
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We survey fundamental concepts for inverse programming and then present the Universal Resolving Algorithm, an algorithm for inverse computation in a first order, functional programming language. We discuss the key concepts of the algorithm, including a three step approach based on the notion of a perfect process tree, and demonstrate our implementation with several examples of inverse computation.
Optimizing criteria for choosing a confidence set for a parameter are formulated as mathematical programming problems. The two optimizing criteria, probability of coverage and size of set, give rise to a pair of inver...
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Optimizing criteria for choosing a confidence set for a parameter are formulated as mathematical programming problems. The two optimizing criteria, probability of coverage and size of set, give rise to a pair of inverse programming problems. Several examples are worked out. The programming problems are then formulated to allow the incorporation of partial information about the parameter. By varying the family of prior distributions, a continuum of problems from the frequency approach to a Bayesian approach is obtained. Some examples are considered in which the family of priors contains more than one but not all prior distributions.
To impute the function of a variational inequality and the objective of a convex optimization problem from observations of (nearly) optimal decisions, previous approaches constructed inverse programming methods based ...
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To impute the function of a variational inequality and the objective of a convex optimization problem from observations of (nearly) optimal decisions, previous approaches constructed inverse programming methods based on solving a convex optimization problem [17,7]. However, we show that, in addition to requiring complete observations, these approaches are not robust to measurement errors, while in many applications, the outputs of decision processes are noisy and only partially observable from, e.g., limitations in the sensing infrastructure. To deal with noisy and missing data, we formulate our inverse problem as the minimization of a weighted sum of two objectives: 1) a duality gap or Karush Kuhn Tucker (KKT) residual, and 2) a distance from the observations robust to measurement errors. In addition, we show that our method encompasses previous ones by generating a sequence of Pareto optimal points (with respect to the two objectives) converging to an optimal solution of previous formulations. To compare duality gaps and KKT residuals, we also derive new sub-optimality results defined by KKT residuals. Finally, an implementation framework is proposed with applications to delay function inference on the road network of Los Angeles, and consumer utility estimation in oligopolies. (C) 2016 Elsevier Inc. All rights reserved.
Duals of bilinear programming problems are used to establish some optimality properties of probability coverage optimization problems. These problems include confidence interval problems and hypothesis testing problem...
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Duals of bilinear programming problems are used to establish some optimality properties of probability coverage optimization problems. These problems include confidence interval problems and hypothesis testing problems in particular cases.
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