Topic
Bilinear program
About: Bilinear program is a research topic. Over the lifetime, 64 publications have been published within this topic receiving 2811 citations.
Papers published on a yearly basis
Papers
TL;DR: A probabilistic framework to design an N-1 secure day-ahead dispatch and determine the minimum cost reserves for power systems with wind power generation is proposed and a reserve strategy according to which the reserves are deployed in real-time operation is identified.
Abstract: We propose a probabilistic framework to design an N-1 secure day-ahead dispatch and determine the minimum cost reserves for power systems with wind power generation. We also identify a reserve strategy according to which we deploy the reserves in real-time operation, which serves as a corrective control action. To achieve this, we formulate a stochastic optimization program with chance constraints, which encode the probability of satisfying the transmission capacity constraints of the lines and the generation limits. To incorporate a reserve decision scheme, we take into account the steady-state behavior of the secondary frequency controller and, hence, consider the deployed reserves to be a linear function of the total generation-load mismatch. The overall problem results in a chance constrained bilinear program. To achieve tractability, we propose a convex reformulation and a heuristic algorithm, whereas to deal with the chance constraint we use a scenario-based-approach and an approach that considers only the quantiles of the stationary distribution of the wind power error. To quantify the effectiveness of the proposed methodologies and compare them in terms of cost and performance, we use the IEEE 30-bus network and carry out Monte Carlo simulations, corresponding to different wind power realizations generated by a Markov chain-based model.
286 citations
TL;DR: A cutting plane algorithm is proposed to solve a special class of nonconvex quadratic program referred to as a bilinear program in the literature and the preliminary results of numerical experiments are encouraging.
Abstract: This paper addresses itself to a special class of nonconvex quadratic program referred to as a bilinear program in the literature. We will propose here a cutting plane algorithm to solve this class of problems. The algorithm is along the lines of H. Tui and K. Ritter, but it differs in its exploitation of the special structure of the problem. Though the algorithm is not guaranteed at this stage of the research to converge to a global optimum, the preliminary results of numerical experiments are encouraging.
267 citations
TL;DR: This work is based on a precise norm-dependent explicit closed form for the projection of a point on a plane that is used to formulate the separating-plane problem as a minimization of a convex function on a unit sphere in a norm dual to that of the arbitrary norm used.
189 citations
TL;DR: This paper identifies some special cases of this mixed-integer bilinear programming problem which are relatively more readily solvable, even though their continuous relaxations are still nonconvex, and designs a composite Lagrangian relaxation-implicit enumeration-cutting plane algorithm.
Abstract: This paper addresses a class of problems called mixed-integer bilinear programming problems. These problems are identical to the well known bilinear programming problems with the exception that one set of variables is restricted to be binary valued, and they arise in various production, location—allocation, and distribution application contexts. We first identify some special cases of this problem which are relatively more readily solvable, even though their continuous relaxations are still nonconvex. For the more general case, we employ a linearization technique and design a composite Lagrangian relaxation-implicit enumeration-cutting plane algorithm. Extensive computational experience is provided to test the efficacy of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm.
108 citations
TL;DR: This work establishes various properties of this extended complementarity problem, which include the convexity of the bilinear objective function under a monotonicity assumption, the polyhedrality ofThe solution set of a monotone XLCP, and an error bound result for a nondegenerate XLCPs.
Abstract: We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity of the bilinear objective function under a monotonicity assumption, the polyhedrality of the solution set of a monotone XLCP, and an error bound result for a nondegenerate XLCP. We also present a finite, sequential linear programming algorithm for solving the nonmonotone XLCP.
92 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 2 |
| 2021 | 1 |
| 2020 | 5 |
| 2019 | 1 |
| 2018 | 7 |
| 2017 | 3 |