A method for convex curve approximation

Article Abstract:

A block sandwich algorithm for convex curve approximation that uses two convex piecewise linear functions is introduced. The procedure, which is illustrated by approximating the efficient frontier of a bi-criteria convex quadratic network program, features a quadratic convergence property which holds the total number of scalar optimization problems required to reach a specified error is less than the constant multiple of the square root of the inverse of the given error.

Operations Research, Convex domains, Approximation theory, Approximation

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Analytic efficient solution set for multi-criteria quadratic programs

Article Abstract:

The derivation of the exact efficient solution set to multicriteria convex quadratic programming problems with linear constraints and three or more objectives was investigated. Specifically, active set schemes for computing the efficient solution set and efficient point set for bi-criteria and multicriteria cases were developed. The procedures were based on the fact that a point is an efficient solution of convex programs if and only if it solves a scalarized problem.

Multiple criteria decision making, Quadratic programming, Convex programming

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Vector equilibrium problem and vector optimization

Article Abstract:

A study was conducted to analyze the vector equilibrium framework based on a vector cost consideration. The idea of parametric equilibria was utilized to establish relations with parametric complementarity and variational inequality problems. Relations with vector optimization problems via scalarization methods were then given under appropriate conditions. Finally, solution techniques for solving vector equilibrium problems were discussed.

Analysis, Mathematical optimization, Optimization theory

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