In this article, we consider the space of all the linear semi-infinite programming (LSIP) problems with a given infinite compact Hausdorff index set, a given number of variables and continuous coefficients, endowed wi...
详细信息
In this article, we consider the space of all the linear semi-infinite programming (LSIP) problems with a given infinite compact Hausdorff index set, a given number of variables and continuous coefficients, endowed with the topology of the uniform convergence. These problems are classified as inconsistent, solvable with bounded optimal set, bounded (i.e. finite valued), but either unsolvable or having an unbounded optimal set, and unbounded (i.e. with infinite optimal value), giving rise to the so-called refined primal partition of the space of problems. The mentioned LSIP problems can be also classified with a similar criterion applied to the corresponding Haar's dual problems, which provides the refined dual partition of the space of problems. We characterize the interior of the elements of the refined primal and dual partitions as well as the interior of the intersections of the elements of both partitions (the so-called refined primal-dual partition). These characterizations allow to prove that most (primal or dual) bounded problems have simultaneously primal and dual non-empty bounded optimal set. Consequently, most bounded continuous LSIP problems are primal and dual solvable.
In this paper, an unconstrained convex programming dual approach for solving a class of linear semi-infinite programming problems is proposed. Both primal and dual convergence results are established under some basic ...
详细信息
In this paper, an unconstrained convex programming dual approach for solving a class of linear semi-infinite programming problems is proposed. Both primal and dual convergence results are established under some basic assumptions. Numerical examples are also included to illustrate this approach.
Presented were a scheme for natural recursive description of the multilinear problem and a phase method for its solution based on the decomposition into a sequence of linear problems with maximal use of the extension ...
详细信息
Presented were a scheme for natural recursive description of the multilinear problem and a phase method for its solution based on the decomposition into a sequence of linear problems with maximal use of the extension of degrees of freedom of each phase. The paper opens a series of two papers.
Obstruction challenges faced in many oil and gas wells, particularly in milling operations, can be leveraged by using mathematical optimization of E-line technology for faster, safer and more accurate well interventio...
详细信息
This paper presents an optimal power flow dispatching for a grid-connected photovoltaic-battery energy storage system under grid-scheduled load-shedding to explore solar energy sufficiently and to benefit the electric...
详细信息
A swarm-exploring neurodynamic network (SENN) based on a two-timescale model is proposed in this study for solving nonconvex nonlinear programming problems. First, by using a convergent-differential neural network (CD...
详细信息
A swarm-exploring neurodynamic network (SENN) based on a two-timescale model is proposed in this study for solving nonconvex nonlinear programming problems. First, by using a convergent-differential neural network (CDNN) as a local quadratic programming (QP) solver and combining it with a two-timescale model design method, a two-timescale convergent-differential (TTCD) model is exploited, and its stability is analyzed and described in detail. Second, swarm exploration neurodynamics are incorporated into the TTCD model to obtain an SENN with global search capabilities. Finally, the feasibility of the proposed SENN is demonstrated via simulation, and the superiority of the SENN is exhibited through a comparison with existing collaborative neurodynamics methods. The advantage of the SENN is that it only needs a single recurrent neural network (RNN) interact, while the compared collaborative neurodynamic approach (CNA) involves multiple RNN runs.
A very surprising result is derived in this paper, that there exists a family of LP duals for general NLP problems. A general dual problem is first derived from implied constraints via a simple bounding technique. It ...
详细信息
A very surprising result is derived in this paper, that there exists a family of LP duals for general NLP problems. A general dual problem is first derived from implied constraints via a simple bounding technique. It is shown that the Lagrangian dual is a special case of this general dual and that other special cases turn out to be LP problems. The LP duals provide a very powerful computational device but are derived using fairly strict conditions. Hence, they can often be infeasible even if the primal NLP problem is feasible and bounded. Many directions for relaxing these conditions are outlined for future research. A concept of local duality is also introduced for the first time akin to the concept of local optimality. (C) 1999 Elsevier Science B.V. All rights reserved.
We analyse the primal-dual states in linear semi-infinite programming (LSIP), where we consider the primal problem and the so called Haar's dual problem. Any linear programming problem and its dual can be classifi...
详细信息
We analyse the primal-dual states in linear semi-infinite programming (LSIP), where we consider the primal problem and the so called Haar's dual problem. Any linear programming problem and its dual can be classified as bounded, unbounded or inconsistent, giving rise to nine possible primal-dual states, which are reduced to six by the weak duality property. Recently, Goberna and Todorov have studied this partition and its stability in continuous LSIP in a series of papers [M. A. Goberna and M. I. Todorov, Primal, dual and primal-dual partitions in continuous linear semi-infinite programming, Optimization 56 (2007), pp. 617-628;M. A. Goberna and M. I. Todorov, Generic primal-dual solvability in continuous linear semi-infinite programming, Optimization 57 (2008), pp. 239-248]. In this article we consider the general case, with no continuity assumptions, discussing the maintenance of the primal-dual state of the problem by allowing small perturbations of the data. We characterize the stability of all of the six possible primal-dual states through necessary and sufficient conditions which depend on the data, and can be easily checked, showing some differences with the continuous case. These conditions involve the strong Slater constraint qualification, and some distinguished convex sets associated to the data.
Murty's algorithm for the linear complementarity problem is generalized to solve the optimality conditions for linear and convex quadratic programming problems with both equality and inequality constraints. An imp...
详细信息
Murty's algorithm for the linear complementarity problem is generalized to solve the optimality conditions for linear and convex quadratic programming problems with both equality and inequality constraints. An implementation is suggested which provides both efficiency and tight error control. Numerical experiments as well as field tests in various applications show favorable results.
Aiming at the problems of short-term overload of power distribution equipment capacity, large operation loss and low accommodation of new energy under the independent operation mode of traditional low-voltage station ...
详细信息
暂无评论