In this paper an exterior point polynomialtimealgorithm for convex quadratic programming problems is proposed. We convert a convex quadratic program into an unconstrained convex program problem with a self-concordan...
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In this paper an exterior point polynomialtimealgorithm for convex quadratic programming problems is proposed. We convert a convex quadratic program into an unconstrained convex program problem with a self-concordant objective function. We show that, only with duality, the Path-following method is valid. The computational complexity analysis of the algorithm is given.
We give the first polynomial-time algorithm for solving the linear complementarity problem with tridiagonal or, more generally, Hessenberg P-matrices. (C) 2012 Elsevier B.V. All rights reserved.
We give the first polynomial-time algorithm for solving the linear complementarity problem with tridiagonal or, more generally, Hessenberg P-matrices. (C) 2012 Elsevier B.V. All rights reserved.
Given ann × n matrixM and ann-dimensional vectorq, the problem of findingn-dimensional vectorsx andy satisfyingy = Mx + q, x ≥ 0,y ≥ 0,x i y i = 0 (i = 1, 2,?,n) is known as a linear complementarity problem...
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Given ann × n matrixM and ann-dimensional vectorq, the problem of findingn-dimensional vectorsx andy satisfyingy = Mx + q, x ≥ 0,y ≥ 0,x i y i = 0 (i = 1, 2,?,n) is known as a linear complementarity problem. Under the assumption thatM is positive semidefinite, this paper presents an algorithm that solves the problem in O(n 3 L) arithmetic operations by tracing the path of centers,{(x, y) ∈ S: x i y i =μ (i = 1, 2,?,n) for some μ > 0} of the feasible regionS = {(x, y) ≥ 0:y = Mx + q}, whereL denotes the size of the input data of the problem.
In this paper, the optimal design of reliability indices in an electrical distribution system and their impact to planning are studied. By formulating the cost due to interrupted KVA-hour, initial interruption cost, a...
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In this paper, the optimal design of reliability indices in an electrical distribution system and their impact to planning are studied. By formulating the cost due to interrupted KVA-hour, initial interruption cost, and modification cost in terms of component reliability indices, an optimization problem is derived while simultaneously considering multiple load points and feeder capacity limits, resulting in a nonlinear programming problem. To solve this nonlinear programming problem, an effective polynomial-time algorithm is presented. The numerical test shows that not only significant savings can be achieved, but also information on identifying value-saving feeder/components can be revealed as well. This is a valuable tool to distribution planning/operations. (C) 2003 Elsevier Science Ltd. All rights reserved.
Efficiently devising optimal offers for Generation Companies (GenCos) in Day-Ahead Electricity Markets is a challenging task. Most solution procedures found in technical literature are built upon non-convex optimizati...
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Efficiently devising optimal offers for Generation Companies (GenCos) in Day-Ahead Electricity Markets is a challenging task. Most solution procedures found in technical literature are built upon non-convex optimization structures, known as Mathematical Programming with Equilibrium Constraints (MPECs), that are difficult to scale to realistic-size instances. Therefore, the main objective of this work is to propose an efficient procedure to aid GenCos to devise optimal offering strategies in Day-Ahead Electricity Markets composed of a single bidding area. Supported by a set of technical results and strong duality theory, a tailored procedure that can be executed in polynomial-time in the number of firms is constructed with global-optimality guarantees. Numerical experiments are conducted, benchmarking the proposed approach against the standard MPEC-derived procedure typically found in the technical literature to solve the offering problem. We found that the proposed solution approach grows (roughly) linearly with the instance size and significantly overcomes (in the order of 20-25 times faster) its counterpart in the most demanding instances. Furthermore, the scalability of the MPEC-derived procedure is challenged even for medium-scale instances, whilst the proposed polynomial-time procedure was able to handle all instances in a reasonable computational time.
We consider the independent set problem, a classical NP-hard optimization problem that remains hard even under substantial restrictions on the input graphs. The complexity status of the problem is unknown for the clas...
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ISBN:
(纸本)9783030307868;9783030307851
We consider the independent set problem, a classical NP-hard optimization problem that remains hard even under substantial restrictions on the input graphs. The complexity status of the problem is unknown for the classes of P-k-free graphs for all k >= 7 and for the class of even-hole-free graphs, that is, graphs not containing any even induced cycles. Using the technique of augmenting graphs we show that the independent set problem is solvable in polynomialtime in the class of even-hole-free graphs not containing an induced path on 10 vertices. Our result is developed in the context of the more general class of {P-10, C-4, C-6}-free graphs.
This paper is concerned with a subclass of deterministic pushdown transducers, called deterministic restricted one-counter transducers (droct's), and studies the equivalence problem for real-time droct's which...
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ISBN:
(纸本)9780769550053
This paper is concerned with a subclass of deterministic pushdown transducers, called deterministic restricted one-counter transducers (droct's), and studies the equivalence problem for real-time droct's which accept by final state. After providing some properties of these droct's, we present a polynomial-time algorithm for checking the equivalence for these droct's.
The dominating induced matching problem is the problem of determining whether a graph has an induced matching that dominates every edge of the graph. This is known to be NP-complete in general. We develop a polynomial...
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The paper is concerned with the two-machine flow shop, where each job needs storage space (a buffer requirement) during the entire time of its processing. The buffer requirement is determined by the duration of job...
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ISBN:
(纸本)9783030226299;9783030226282
The paper is concerned with the two-machine flow shop, where each job needs storage space (a buffer requirement) during the entire time of its processing. The buffer requirement is determined by the duration of job's first operation. The goal is to minimise the time needed for the completion of all jobs. This scheduling problem is NP-hard in the strong sense even for very restricted cases such as the case with a given order of jobs processing on one of the machines. The paper contributes to the efforts of establishing the borderline between the NP-hard and polynomial-time solvable cases by proving that there exists a polynomial-time algorithm which constructs an optimal schedule if the duration of each operation does not exceed one-fifth of the buffer capacity. The presented polynomial-time algorithm is used as a basis for a heuristic for the general case. This heuristic is complemented by a Lagrangian relaxation based heuristic and a bin-packing based constructive heuristic. The heuristics are tested by computational experiments.
In this paper we generalize N-fold integer programs and two-stage integer programs with AT scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer program...
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ISBN:
(纸本)9783642130359
In this paper we generalize N-fold integer programs and two-stage integer programs with AT scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time solvable for any linear objective. Moreover, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any convex separable objective function. We conclude with two sample applications, stochastic integer programs with second-order dominance constraints and stochastic integer multi-commodity flows, which (for fixed blocks) can be solved in polynomialtime in the number of scenarios and commodities and in the binary encoding length of the input data. In the proof of our main theorem we combine several non-trivial constructions from the theory of Graver bases. We are confident that our approach paves the way for further extensions.
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