In this paper, we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas. For a given feasible point of a convex separable program, the inverse optimization is to determine whether the feasible...

When using interior point methods for solving semidefinite programs (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, we propose a trust region algorithm for solving...

A continuous approach using NCP function for approximating the solution of the max-cut problem is proposed. The max-cut problem is relaxed into an equivalent nonlinearly constrained continuous optimization problem and a feasible direction method without line searches is presented for generating...

In this paper we consider problems of the following type: Let E = { e 1 , e 2 ,..., e n } be a finite set and $${\mathcal {F}}$$ be a family of subsets of E. For each element e i in E, c i is a given capacity and $${\mathcal {w}}$$ i is the cost of increasing capacity c i by one unit. It is...

A new smoothing approach was given for solving the mathematical programs with complementarity constraints (MPCC) by using the aggregation technique. As the smoothing parameter tends to zero, if the KKT point sequence generated from the smoothed problems satisfies the second-order necessary...

A new smoothing approach was given for solving the mathematical programs with complementarity constraints (MPCC) by using the aggregation technique. As the smoothing parameter tends to zero, if the KKT point sequence generated from the smoothed problems satisfies the second-order necessary...

In this paper we consider problems of the following type: Let E = { e <Subscript>1</Subscript>, e <Subscript>2</Subscript>,..., e <Subscript> n </Subscript> } be a finite set and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal {F}}$$</EquationSource> </InlineEquation> be a family of subsets of E. For each element e <Subscript> i </Subscript> in E, c <Subscript> i </Subscript> is a given capacity and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$${\mathcal {w}}$$</EquationSource> </InlineEquation> <Subscript> i </Subscript> is the cost of increasing capacity c <Subscript> i </Subscript> by one...</subscript></subscript></equationsource></inlineequation></subscript></subscript></equationsource></inlineequation></subscript></subscript></subscript>

We consider an inverse quadratic programming (QP) problem in which the parameters in both the objective function and the constraint set of a given QP problem need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a linear...

Given a networkN=(V,A,c), a sources εV, a. sinkt εV and somes —t cuts and suppose each element of the capacity vectorc can be changed with a cost proportional to the changes, the inverse problem of minimum cuts we study here is to change the original capacities with the least total cost...