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 <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>