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Duality and optimality conditions for reverse convex programs via a convex decomposition
In this paper via the so-called Fenchel–Lagrange duality, we provide necessary local optimality conditions for a reverse convex programming problem
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Lagrange Multipliers in Locally Convex Spaces
We give a general Lagrange multiplier rule for mathematical programming problems in a Hausdorff locally convex space. We consider infinitely many...
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A global interior point method for nonconvex geometric programming
The strategy presented in this paper differs significantly from existing approaches as we formulate the problem as a standard optimization problem of...
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Computing Critical Angles Between Two Convex Cones
This paper addresses the numerical computation of critical angles between two convex cones in Euclidean spaces. We present a novel approach to...
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Convex Generalized Differentiation
This chapter is devoted to basic constructions of convex generalized differentiation. Using the separation theorems and the intersection rule for...
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Preliminaries: Convex Analysis and Convex Programming
In this chapter, some definitions and results connected with convex analysis, convex programming, and Lagrangian dualityLagrangian duality (see...
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Convex projection and convex multi-objective optimization
In this paper we consider a problem, called convex projection, of projecting a convex set onto a subspace. We will show that to a convex projection...
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Robust Bond Portfolio Construction via Convex–Concave Saddle Point Optimization
The minimum (worst case) value of a long-only portfolio of bonds, over a convex set of yield curves and spreads, can be estimated by its...
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Lagrange Multipliers, Duality, and Sensitivity in Set-Valued Convex Programming via Pointed Processes
We present a new kind of Lagrangian duality theory for set-valued convex optimization problems whose objective and constraint maps are defined...
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Improved Convex and Concave Relaxations of Composite Bilinear Forms
Deterministic nonconvex optimization solvers generate convex relaxations of nonconvex functions by making use of underlying factorable...
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Conic Linear Programming Duals for Classes of Quadratic Semi-Infinite Programs with Applications
In this paper, we first present strong conic linear programming duals for convex quadratic semi-infinite problems with linear constraints and...
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On tackling reverse convex constraints for non-overlap** of unequal circles
We study the unequal circle-circle non-overlap** constraints, a form of reverse convex constraints that often arise in optimization models for...
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An outer approximation algorithm for generating the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems
In this paper, we present an outer approximation algorithm for computing the Edgeworth–Pareto hull of multi-objective mixed-integer linear...
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General convex relaxations of implicit functions and inverse functions
Convex relaxations of nonconvex functions provide useful bounding information in applications such as deterministic global optimization and...
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Duality for convex infinite optimization on linear spaces
This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of...
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Equilibrium modeling and solution approaches inspired by nonconvex bilevel programming
Methods for finding pure Nash equilibria have been dominated by variational inequalities and complementarity problems. Since these approaches...
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Strong Duality and Solution Existence Under Minimal Assumptions in Conic Linear Programming
Conic linear programs in locally convex Hausdorff topological vector spaces are addressed in this paper. Solution existence for the dual problem, as...