An algorithm is proposed for locating an optimal solution satisfying the KKT conditions to a specified tolerance to inequality-path-constrained dynamic optimization (PCDO) problem within finite iterations. This algori...
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An algorithm is proposed for locating an optimal solution satisfying the KKT conditions to a specified tolerance to inequality-path-constrained dynamic optimization (PCDO) problem within finite iterations. This algorithm solves the optimization problem by iteratively approximating the original optimization problem through adaptive convexification of its lower level programs. In the process of convexification of the lower level programs, alpha BB technique is used adaptively to construct convex relaxations of a path constraint in each time subinterval. Compared to the result in (Fu, Faust, Chachuat, & Mitsos, 2015), the distinguishing feature is that the proposed algorithm avoids numerically solving the non-convex lower level program to global optimality at each iteration. Two numerical examples are shown to demonstrate the performance of the algorithm. (C) 2021 Elsevier Ltd. All rights reserved.
We present a novel methodology for the simultaneous robust design and scheduling of controlled environment agricultural (CEA) systems under multi-period risk. This problem is formulated as a semi-infinite program with...
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We present a novel methodology for the simultaneous robust design and scheduling of controlled environment agricultural (CEA) systems under multi-period risk. This problem is formulated as a semi-infinite program with several semi-infinite constraints pertaining to mean-variance risk exposure with uncertain covariance over each period in the planning horizon. The general model enables robust optimization of CEA systems for cultivation of any crop portfolio under any number of cultivation modes, with a solution that represents an optimal design and operating schedule that is robust to worst-case uncertainty. Therefore, this methodology provides a conservative basis for engineering and investment decision-making and represents, to our knowledge, the first robust optimization approach to CEA systems. Our approach effectively increases the robustness of CEA systems to market uncertainty, improves the long-term economics of CEA systems over naive operating strategies, and validates the economic viability of single and multi-mode CEA production of distinct crop portfolios. (C) 2021 Elsevier Ltd. All rights reserved.
The use of autonomous buses increases, and their operations increasingly intertwine with other public transport lines. At the same time, the use of autonomous buses in a mixed traffic environment induces new challenge...
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ISBN:
(纸本)9781728141497
The use of autonomous buses increases, and their operations increasingly intertwine with other public transport lines. At the same time, the use of autonomous buses in a mixed traffic environment induces new challenges with respect to their service synchronization with other lines. In fact, due to their cautious driving behavior in a mixed environment, the operations of autonomous buses show a high degree of variation in inter-station travel times, which leads to many unsuccessful transfers. Many tactical planning problems, however, naively assume that this uncertainty can be reduced to a single deterministic value (e.g., a travel time expectation). In this study, we propose a technique to find a robust schedule of dispatching and holding times that incorporates the inherent uncertainty in the operations. We discuss the complexity and applicability of such robust problems in public transit operations in general, and solve the optimization problem for an autonomous bus system that serves as a feeder line to a collector line. The numerical experiments show that the robust rescheduling and holding solution is resilient to variations in travel times: the operations maintain a high level of service regularity and avoid missed passenger transfers even under extreme scenarios.
This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniqu...
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This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniques based on completeness and limiting procedures. The main attention is paid to generalized derivatives and subdifferentials of the Dini-Hadamard type with the usage of mild qualification conditions revolving around metric subregularity. In this way we develop calculus rules of generalized differentiation in normed spaces without imposing restrictive normal compactness assumptions and the like and then apply them to general problems of constrained optimization. Most of the obtained results are new even in finite dimensions. Finally, we derive refined necessary optimality conditions for nonconvex problems of semi-infinite and semidefinite programming.
In this paper, we introduce the concept of higher-order (phi, )-V-invexity and present two types of higher-order dual models for a semi-infinite minimax fractional programming problem. Weak, strong, and strict convers...
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In this paper, we introduce the concept of higher-order (phi, )-V-invexity and present two types of higher-order dual models for a semi-infinite minimax fractional programming problem. Weak, strong, and strict converse duality theorems are discussed under the assumptions of higher-order (phi, )-V-invexity to establish a relation between the primal and dual problems.
Using techniques of variational analysis, necessary and sufficient subdifferential conditions for Holder error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an applicati...
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Using techniques of variational analysis, necessary and sufficient subdifferential conditions for Holder error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an application, we consider the setting of convex semi-infinite optimization and give a characterization of the Holder calmness of the argmin mapping in terms of the level set mapping (with respect to the objective function) and a special supremum function. We also estimate the Holder calmness modulus of the argmin mapping in the framework of linear programming.
This paper deals with nonsmooth semi-infinite programming problem which in recent years has become an important field of active research in mathematical programming. A semi-infinite programming problem is characterize...
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This paper deals with nonsmooth semi-infinite programming problem which in recent years has become an important field of active research in mathematical programming. A semi-infinite programming problem is characterized by an infinite number of inequality constraints. We formulate Wolfe as well as Mond-Weir type duals for the nonsmooth semi-infinite programming problem and establish weak, strong and strict converse duality theorems relating the problem and the dual problems. To the best of our knowledge such results have not been done till now.
We study an optimization program over nonnegative Borel measures that encourages sparsity in its solution. Efficient solvers for this program are in increasing demand, as it arises when learning from data generated by...
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We study an optimization program over nonnegative Borel measures that encourages sparsity in its solution. Efficient solvers for this program are in increasing demand, as it arises when learning from data generated by a "continuum-of-subspaces" model, a recent trend with applications in signal processing, machine learning, and high-dimensional statistics. We prove that the conditional gradient method (CGM) applied to this infinite-dimensional program, as proposed recently in the literature, is equivalent to the exchange method (EM) applied to its Lagrangian dual, which is a semi-infinite program. In doing so, we formally connect such infinite-dimensional programs to the well-established field of semi-infinite programming. On the one hand, the equivalence established in this paper allows us to provide a rate of convergence for the EM that is more general than those existing in the literature. On the other hand, this connection and the resulting geometric insights might in the future lead to the design of improved variants of the CGM for infinite-dimensional programs, which has been an active research topic. The CGM is also known as the Frank-Wolfe algorithm.
In this paper we apply two convexification procedures to the Lagrangian of a nonconvex semi-infinite programming problem. Under the reduction approach it is shown that, locally around a local minimizer, this problem c...
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In this paper we apply two convexification procedures to the Lagrangian of a nonconvex semi-infinite programming problem. Under the reduction approach it is shown that, locally around a local minimizer, this problem can be transformed equivalently in such a way that the transformed Lagrangian fulfills saddle point optimality conditions, where for the first procedure both the original objective function and constraints (and for the second procedure only the constraints) are substituted by their pth powers with sufficiently large power p. These results allow that local duality theory and corresponding numerical methods (e.g. dual search) can be applied to a broader class of nonconvex problems.
The Laplace-Stieltjes transform of a matrix-exponential (ME) distribution is a rational function where at least one of its poles of maximal real part is real and negative. The coefficients of the numerator polynomial,...
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The Laplace-Stieltjes transform of a matrix-exponential (ME) distribution is a rational function where at least one of its poles of maximal real part is real and negative. The coefficients of the numerator polynomial, however, are more difficult to characterise. It is known that they are contained in a bounded convex set that is the intersection of an uncountably infinite number of linear half-spaces. In order to determine whether a given vector of numerator coefficients is contained in this set (i.e. the vector corresponds to an ME distribution) we present a semi-infinite programming algorithm that minimises a convex distance function over the set. In addition, in the event that the given vector does not correspond to an ME distribution, the algorithm returns a closest vector which does correspond to one.
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